A drawer contains 12 brown socks and 12 black socks, all unmatched. A man takes socks out at random in the dark. Answer the following questions. Question 7 Select the least number of socks that he must take out to be sure that he has at least two socks of the same color. 12 4 Question 8 Select the least number of socks that he must take out to be sure that he has at least two black socks. 3

If we use alpha as the criteria or critical value for the maximum probability of incorrectly rejecting the null hypothesis, then when the p-value is less than alpha, the null hypothesis is rejected.

If we use alpha as the criteria or critical value for the maximum probability of incorrectly rejecting the null hypothesis, then when the p-value is less than alpha, the null hypothesis is rejected. This means that there is strong evidence to suggest that the alternative hypothesis is true and that the data set supports this conclusion. Therefore, we can conclude that the null hypothesis is not supported by the data and that we can reject it.
If we use alpha as the criteria or critical value for the maximum probability of incorrectly rejecting the null hypothesis, then when the p-value is less than alpha, the null hypothesis is rejected.

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The average number of grams of fat per ounce of meat or fish consumed by a person over a 5 day period, using the weighted mean, is 2.72 g/oz.

To find the weighted mean of the average number of grams of fat per ounce of meat or fish consumed by a person over a 5 day period, we need to multiply each fat (g/oz) value by its corresponding weight and then add them all up.

Here's how to do it:

- Fried shrimp: 3 oz x 3.33 g/oz = 9.99 g
- Veal cutlet: 3.33 oz x 3 g/oz = 9.99 g
- Roast beef: 2 oz x 2.5 g/oz = 5 g
- Fried chicken: 2.5 oz x 4.4 g/oz = 11 g
- Canned tuna: 4 oz x 1.75 g/oz = 7 g

Next, add up all the total grams of fat consumed:

9.99 + 9.99 + 5 + 11 + 7 = 42.98 g

Finally, divide the total grams of fat by the total weight of meat and fish consumed:

(3 + 3.33 + 2 + 2.5 + 4) = 15.83 oz

42.98 g ÷ 15.83 oz = 2.72 g/oz

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(a) This statement is false. The probability of getting heads or tails on a fair coin is always 50%, regardless of previous outcomes.  

(b) This statement is true. Drawing a face card and drawing a red card from a full deck of playing cards are mutually exclusive events.

(a) The statement is false. The outcome of each coin toss is independent of the previous tosses. Therefore, the chance of getting heads on the next toss is still 50%, regardless of the outcome of the previous eight tosses.

(b) The events of drawing a face card and drawing a red card are not mutually exclusive events. There are 12 face cards in a deck of playing cards, and 6 of them are red (2 jacks, 2 queens, and 2 kings). Therefore, the probability of drawing a face card and a red card from a full deck of playing cards is:

P(face card and red card) = P(face card) x P(red card|face card)
P(face card and red card) = (12/52) x (6/12)
P(face card and red card) = 3/52 or about 5.77%

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The range would increase by 1 when the age of 17 is added to the data

Given data ,

The range is the difference between the highest and lowest values in a data set

In the original data set provided, the highest value is 33 and the lowest value is 18, so the range is 33 - 18 = 15

Now , when the age 17 is added , the new lowest value of the data is 17

So , the new range is R = 33 - 17 = 16

Hence , the range of the data has increased by 1

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To identify outliers for the age-group 40 40 years to 50 50 years, we would need to calculate the interquartile range (iqr) for this age-group separately.

If the three values of 60 60, 62 62, and 84 84 are still more than 1.5 times the iqr greater than the upper quartile or less than the lower quartile, then they would still be considered outliers for this age-group as well. However, it's important to note that outliers can vary depending on the dataset and age-group being analyzed.

To determine which of the values (60, 62, and 84) are identified as outliers for the age-group 40 to 50 years, follow these steps:
1. Calculate the quartiles for the age-group 40 to 50 years. You need the lower quartile (Q1) and the upper quartile (Q3).
2. Compute the interquartile range (IQR) by subtracting Q1 from Q3 (IQR = Q3 - Q1).
3. Identify the lower outlier limit by multiplying the IQR by 1.5 and subtracting it from Q1 (lower limit = Q1 - 1.5 * IQR).
4. Identify the upper outlier limit by multiplying the IQR by 1.5 and adding it to Q3 (upper limit = Q3 + 1.5 * IQR).
5. Check if the values 60, 62, and 84 are below the lower limit or above the upper limit. If so, they are considered outliers for the age-group 40 to 50 years.
Without the actual data for the age-group 40 to 50 years, I cannot provide specific results. Please calculate the quartiles and limits, and then compare the given values to determine the outliers.

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The theoretical probability of the spinner not landing on yellow is 5/8, which is approximately 0.625.

The correct option is B.

The spinner has a total of 8 equally likely outcomes, so the theoretical probability of each individual outcome is 1/8.

To find the probability of the spinner not landing on yellow, we need to add up the probabilities of all the non-yellow outcomes.

These are:

Purple (sections 1 and 8): 2/8 = 1/4

Blue (sections 4, 5, and 6): 3/8

Red (section 7): 1/8

So the probability of the spinner not landing on yellow is:

P(not yellow) = P(purple) + P(blue) + P(red)

= 1/4 + 3/8 + 1/8

= 5/8

= 0.625

So the correct option is (B) 0.625.

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The representations given, as regards whether it shows a quadratic function, is B. No.

To find out if the representations shows a quadratic function, find the first differences between the given y values:

10 - 5 = 5

15 - 10 = 5

20 - 15 = 5

Then, calculate the second differences, using the first differences :

5 - 5 = 0

5 - 5 = 0

The second difference is not the same as the first difference and so this is not a quadratic function.

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the answer for your question is B

The value of c in the equation 6,098×c=5,695,532 is 934

The given equation is 6,098×c=5,695,532

We have to find the value of c

c is the variable in the equation

6,098×c=5,695,532

Divide  both sides by 6098

c=5,695,532/6098

c=934

Hence, the value of c in the equation 6,098×c=5,695,532 is 934

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The height of the cylinderical can is derived to be 7.05 cm to the nearest hundredth.

In calculating for the surface area of a cylinder, we use the formula:

A = 2πrh + 2πr²

From the question;

A = 150 cm²

π = 3.14

r = 5/2 = 2.5 cm

150 cm² = 2 × 3.14 × 2.5 cm × h + 2 × 3.14 × (2.5 cm)²

150 cm² = h15.7 cm + 39.25 cm²

h15.7 cm = 150 cm² - 39.25 cm²

h15.7 cm = 110.75 cm²

h = 110.75 cm²/15.7 cm

h = 7.05 cm

Therefore, the height of the cylinderical can is derived to be 7.05 cm to the nearest hundredth.

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The value of the trigonometric ratio Sin 89 is 0.9998

From the question, we have the following parameters that can be used in our computation:

Sin 89

The trigonometric ratio can be evaluated using a calculator

Using a calculator, we have the following result

Sin 89 = 0.99984769515

Approximate

Sin 89 = 0.9998

Hence, the solution is 0.9998

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The correct definition for a proposition is: a sentence that describes some state of affairs and therefore makes a claim about the world. In this context, a proposition is a statement that asserts something about the world, while an utterance refers to the actual spoken or written expression by a particular speaker on a specific occasion.

A proposition refers to a sentence that describes a particular state of affairs and therefore makes a claim about the world. It is a statement or assertion that can be either true or false. It is different from an utterance, which is the use of a sentence by a particular speaker, on a particular occasion. The proposition is the underlying meaning of the utterance, which can be expressed in different ways depending on the context.

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The statistical procedure you are referring to is known as regression analysis (option d). Regression analysis is a technique used to analyze the relationship between two variables by developing an equation that quantifies their association. This method is widely used in various fields, such as economics, biology, and social sciences, to predict and understand trends, make forecasts, and identify causal relationships.

In a regression analysis, one variable is considered the dependent variable (the outcome), while the other is the independent variable (the predictor). The dependent variable is typically the variable of interest that you want to explain or predict. The independent variable is the factor that may influence the dependent variable.

The procedure involves fitting a line or curve to the data points in a way that minimizes the differences between the observed values and the predicted values. This allows researchers to identify and interpret the underlying patterns and make inferences about the relationship between the variables.

In summary, regression analysis is a powerful statistical procedure used to develop an equation that illustrates how two variables are related. By doing so, it enables researchers to make predictions, assess trends, and understand the causal relationships between variables in various fields

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Under the Laplace model, each of the six sides of the die is equally likely to come up. Therefore, the probability of rolling an even number is equal to the number of even sides (which is three) divided by the total number of sides (which is six). This gives us a probability of 0.5 or 50%.

To explain further, a probability model is a mathematical representation of a random process that assigns probabilities to various outcomes. In this case, the probability model for rolling a six-sided die is that each of the six sides has an equal chance of being rolled. This is called the Laplace model, named after the French mathematician Pierre-Simon Laplace.

When we say that we want to find the probability that the result is even, we are looking for the chance that the die will land on either the 2, 4, or 6 sides. Since there are three even sides out of a total of six possible outcomes, the probability of rolling an even number is 3/6 or 0.5.

In summary, under the Laplace model for rolling a six-sided die, the probability of rolling an even number is 0.5 or 50%.
In this scenario, we are considering a probability model for rolling a six-sided die. Under the Laplace model, we assume that all outcomes are equally likely. Therefore, we can find the probability of rolling an even number by determining the ratio of favorable outcomes to total possible outcomes.

A standard six-sided die has the numbers 1 to 6 on its faces. The even numbers on the die are 2, 4, and 6. So, there are 3 favorable outcomes (rolling an even number) out of 6 possible outcomes (rolling any number from 1 to 6).

To find the probability of rolling an even number, we divide the number of favorable outcomes (3) by the total number of possible outcomes (6):

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

Probability (Even) = 3 / 6

Simplifying the fraction, we get:

Probability (Even) = 1 / 2

Therefore, under the Laplace model, the probability of rolling an even number on a six-sided die is 1/2 or 50%.

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The function d(x) that represents the value of Dyanas truck X years after it's purchase is 15000(0.9)^x

Assuming that the depreciation rate is constant over the years, the function d(x) can be expressed as:

d(x) = 15000(1-0.1)^x

Where x is the number of years since the purchase of the truck.

This can be we can simplified further as: d(x) = 15000(0.9)^x

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To determine whether the mean annual tea consumption in the United States has decreased, we need to conduct a hypothesis test. We can use either a z-test or a t-test, depending on whether the population standard deviation is known or unknown, respectively. In this case, we are given that the population standard deviation is 2.2 gallons, so we can use a z-test.

Our null hypothesis is that the mean annual tea consumption in the United States is equal to 8.9 gallons. Our alternative hypothesis is that the mean annual tea consumption is less than 8.9 gallons. We want to test if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

Using the sample data provided, we calculate a test statistic of -2.45. This is calculated by taking the difference between the sample mean and the hypothesized population mean, divided by the standard error of the mean (which is the population standard deviation divided by the square root of the sample size).

Next, we use a standard normal distribution table to find the p-value associated with our test statistic. The p-value turns out to be 0.0071.

Finally, we compare the p-value to our chosen significance level (usually 0.05 or 0.01) to determine whether we should reject the null hypothesis. In this case, the p-value is less than 0.05, so we reject the null hypothesis and conclude that there is enough evidence to show that the mean annual tea consumption in the United States has decreased.

In conclusion, based on the given sample data, we can conduct a z-test to determine whether the mean annual tea consumption in the United States has decreased. We reject the null hypothesis and conclude that there is enough evidence to support the alternative hypothesis that the mean annual tea consumption has indeed decreased.

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This statement is false.

Every real matrix has real eigenvalues or comes in pairs of complex conjugate eigenvalues.

In general, the eigenvalues of a 2x2 matrix A can be found by solving the characteristic equation det(A - lambda*I) = 0, where I is the 2x2 identity matrix and lambda is the eigenvalue. The characteristic equation is a quadratic equation in lambda, and its solutions are the eigenvalues of A.

For a real 2x2 matrix, the coefficients of the characteristic equation are real, and so the solutions to the characteristic equation are either real or complex conjugate pairs. This follows from the fact that complex roots of real polynomials always come in complex conjugate pairs.

Now, suppose that a real 2x2 matrix A has eigenvalues i and 2i. Since these eigenvalues are not real, they must be complex conjugates of each other. That is, 2i is also an eigenvalue of A, and the other eigenvalue must be the complex conjugate of i, which is -i.

However, the characteristic equation of a 2x2 matrix with eigenvalues i and 2i is given by:

det(A - lambda*I) = (a - lambda)(d - lambda) - bc = (a - lambda)(d - lambda) - b*c

where A = [[a,b],[c,d]], and lambda = i or 2i.

If we substitute lambda = i into the above equation, we get:

(a - i)(d - i) - b*c = 0

Expanding this equation, we get:

ad - ai - di + i^2 - bc = 0

Simplifying, we get:

(ad - bc) - i(a + d) = 0

Since the matrix A has real entries, the imaginary part of this equation must be zero, which implies that a + d = 0. But this contradicts the assumption that A has eigenvalues i and 2i, since the sum of the eigenvalues of A is equal to the trace of A, which is a + d. Therefore, there cannot exist a real 2x2 matrix with eigenvalues i and 2i.

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To calculate the probability, we need to divide the number of deaths (12) by the number of visitors (6.2 million) and multiply by 100 to get a percentage.
Probability = (12/6,200,000) x 100 = 0.00019354838


Given that the Grand Canyon has an average of 6.2 million visitors each year and an average of 12 deaths per year, we can calculate the probability of a visitor's death as follows:

Step 1: Convert the annual number of deaths to a decimal.
12 deaths per year / 6,200,000 visitors per year = 0.0000019355 (rounded to 8 decimal places)
To calculate the probability, we need to divide the number of deaths (12) by the number of visitors (6.2 million) and multiply by 100 to get a percentage.

Probability = (12/6,200,000) x 100 = 0.00019354838

Rounded to eight decimal places, the probability is 0.00019355.

So, the probability that a visitor to the Grand Canyon will die while visiting is 0.00019355(rounded to 8 decimal places). This probability is theoretical because it is based on the average number of deaths and visitors over several years.

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The calculated measure of the angle B is 12 degrees

From the question, we have the following parameters that can be used in our computation:

Using the sum of opposite interior angles, we have

C  = A + B

Substitute the known values in the above equation, so, we have the following representation

6x + 9 + x - 8 = 141

When the like terms are evaluated, we have

7x + 1 141

So, we have

7x = 140

Divide

x = 20

This means that

m∠B=(x − 8)∘

Substitute the known values in the above equation, so, we have the following representation

m∠B=(20 − 8)∘

Evaluate

m∠B = 12∘

Hence, the measure of the angle is 12 degrees

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A test for two proportions and the null hypothesis would be the best test statistic to assess the variance in bacon consumption from 2011 to 2016.

The null hypothesis for the test is that the proportion of adults who consumed at least 3 pounds of bacon in 2011 is equivalent to the proportion of adults who consumed at least three pounds of bacon in 2016.

A potential explanation would be that the percentage of adults who ate at least 3 pounds of bacon in 2011 and 2016 differed.

Additionally, the test statistic may be likened to a chi-squared distribution with one degree of freedom; hence, it is necessary to compute the test statistic's p-value in order to establish whether the null hypothesis can be ideally rejected or not.

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The population of tigers 20 years ago was 106,000 tigers.

Let's say that 20 years ago the population was P, if we reduce this number by 97%, then we will get:

P' = P*(1 - 97%/100%)

P' = P*(1 - 0.97)

P' = P*0.03

We know that the population now is 3200, then P' = 3200

3200 = P*0.03

Solving this equation for P we will get:

P = 3200/0.03 = 106,666.666....

Rounding it to the nearest thousand we get:

P = 106,000

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Since the distance from a point to point C is 1 and the distance from that same point to point B is 4, the point must be: C. point D.

In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

From the number line shown above, we have:

Distance = 4 + (-1)

Distance = 4 - 1

Distance = 3 (point D).

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The correct answer is d) No, because 1.12 < 3.84 for chi-square.

To determine whether a chi-square test based on a 2 x 2 table using a level of 0.05 is statistically significant, we need to compare the chi-square statistic (in this case, 1.12) to the critical value of chi-square with 1 degree of freedom and a significance level of 0.05.

For a 2 x 2 table, the degrees of freedom is (number of rows - 1) multiplied by (number of columns - 1), which equals (2-1) x (2-1) = 1.

Looking at a chi-square distribution table with 1 degree of freedom and a significance level of 0.05, we find the critical value of chi-square to be 3.84.

Since the chi-square statistic (1.12) is less than the critical value (3.84), we fail to reject the null hypothesis and conclude that the results are not statistically significant.

Therefore, correct answer is d) No, because 1.12 < 3.84.

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According to the information, the constant of proportionality is 1/2, the equation that represents the relationship p = (1/2)t, and the points awarded for 18 minutes of play p = (1/2)(18) = 9.

To find the constant of proportionality, we can use the fact that the game awards one-half point for every 1 minute of play. We can set up a proportion:

where,

Simplifying the left side, we get:

Therefore, the constant of proportionality is 1/2.

To write an equation that represents the relationship, we can use the constant of proportionality we found in Part A. Let p be the number of points awarded and t be the amount of time played. Then the equation is:

For 5 minutes or more, the game awards two and one-half points for every 5 minutes of play. Thus, for t ≥ 5, we have:

Thus, the equation that represents the relationship is:

To graph the relationship, we can plot the points (t, p) for different values of t. Because the number of points awarded is proportional to the amount of time played, the points will lie on a straight line that passes through the origin (0, 0). We can plot at least two points to draw the line, such as (1, 1/2) and (5, 2.5).

To find the number of points awarded for 18 minutes of play, we can use the equation we found in Part B:

Substituting t = 18, we get:

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The answer for the equation is B.

150 with a remainder of 2

The slope of the line is -294/25 and the y-intercept is -294/25.

To find the equation of the line through (7,6) that cuts off the least area from the first quadrant, we need to minimize the product of the x and y intercepts.

Let the x-intercept be a and the y-intercept be b. Then the equation of the line is:

y = (-b/a)x + b

The product of the intercepts is ab = b(-6/b) = -6.

To minimize this product, we need to find the values of a and b that satisfy the constraint that the line passes through (7,6).

Substituting y = 6 and x = 7 in the equation of the line, we get:

6 = (-b/a)7 + b

Solving for b, we get:

b = 42/(a+7)

Substituting this value of b in the equation ab = -6, we get:

a(42/(a+7)) = -6

Simplifying, we get:

42a = -6(a+7)

48a = -42

a = -7/8

Substituting this value of a in the equation b = 42/(a+7), we get:

b = 294/25

Therefore, the equation of the line is:

y = (-294/25)x - 294/25

The slope of the line is -294/25 and the y-intercept is -294/25.

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The length of the minor arc is equal to 1.109 centimeters.

In this problem we must compute the length of minor arc, in centimeters, based on central angles, in degrees, and length of major arc, in centimeters. The arc length is directly proportional to the measure of the central angle:

s ∝ θ

Where:

9.4 cm / s = 322° / 38°

s = 1.109 cm

The minor arc has a length of 1.109 centimeters.

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The multinomial theorem states that the expansion of the expression (a+b+c+...+z)^n can be found by summing over all possible ways to choose the exponents of each variable such that their sum is n.

the coefficient of the term with exponents a^x b^y c^z ... z^w is given by the multinomial coefficient:

C(x,y,z,...,w) = n! / (x! y! z! ... w!)

where x+y+z+...+w=n.

In this problem, we are looking for the value of n such that the expansion of the expression (a+b+c+d+1)^n contains exactly 1001 terms that include all four variables a, b, c, and d, each to some positive power. Let's rewrite the expression as (a+b+c+d)^n (1+1)^n, since we know that (1+1)^n = 2^n and does not affect the number of terms with a, b, c, and d.

Using the multinomial theorem, we can expand (a+b+c+d)^n and find the coefficient of each term that includes all four variables. Since each variable must appear with a positive exponent, we can start by looking at the terms where each variable appears with an exponent of 1. There are 4 ways to choose which variable appears first, and for each choice, there are (n choose 1) ways to choose which exponent it has. Then, there are 3 variables left to choose from, and for each choice, there are (n-1 choose 1) ways to choose its exponent. This gives us a total of 4(n choose 1)(n-1 choose 1) = 12n(n-1) terms that include all four variables with positive exponents.

Similarly, we can look at the terms where each variable appears with an exponent of 2. There are (4 choose 2) = 6 ways to choose which two variables appear first, and for each choice, there are (n choose 2) ways to choose their exponents. Then, there are 2 variables left to choose from, and for each choice, there are (n-2 choose 1) ways to choose its exponent. This gives us a total of 6(n choose 2)(n-2 choose 1) = 3n(n-1)(n-2) terms that include all four variables with positive exponents.

Continuing in this way, we can look at the terms where each variable appears with an exponent of 3 or 4, and we find that the total number of terms that include all four variables with positive exponents is:

12n(n-1) + 3n(n-1)(n-2) + 4(n choose 3)(n-3) + (n choose 4)

We want this expression to be equal to 1001, so we can solve for n using the answer choices:

(a) 9: 12(9)(8) + 3(9)(8)(7) + 4(9 choose 3)(6) + (9 choose 4) = 3424, which is too large

(b) 14: 12(14)(13) + 3(14)(13)(12) + 4(14 choose 3)(11) + (14 choose 4) = 1001, so the answer is (b) 14.

Therefore, n=14 is the value that gives us exactly 1001 terms that include all four variables a, b, c, and d, each to some positive power.

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The population mean time on death row is different than 15 years with p value is 0.0002.

To conduct the hypothesis test, we will use a one-sample t-test with the following null and alternative hypotheses:

Null hypothesis: The population mean time on death row is equal to 15 years. μ = 15

Alternative hypothesis: The population mean time on death row is different than 15 years. μ ≠ 15

We will use a significance level of 0.05.

First, we need to calculate the t-value:

t = (x - μ) / (s / √n)

t = (17.4 - 15) / (6.3 / √75)

t = 3.667

Next, we need to find the degrees of freedom:

df = n - 1

df = 74

Using an online calculator for the t-distribution, we find that the p-value for a two-tailed test with a t-value of 3.667 and 74 degrees of freedom is less than 0.00015 (or 0.0002 when rounded to 4 decimal places).

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the population mean time on death row is different than 15 years.

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