A two-sample tt-test for a difference in means will be conducted to investigate whether the average amount of money spent per customer at Department Store M is different from that at Department Store V. From a random sample of 35 customers at Store M, the average amount spent was $300 with standard deviation $40. From a random sample of 40 customers at Store V, the average amount spent was $290 with standard deviation $35. Assuming a nuk hypothesis of no difference in population means, which of the following is the test statistic for the appropriate test to investigate whether there is a difference in population means Department Store M minus Department Store V?
A. t= √300-290 /35^2/40 + 40^2/35
B. t = 300-290 / √40^2 +35^2 / 35+40
C. t= 300-290 / √40+35 / 35+40
D. t= 300-290 / √40^2 /35 +35^2/ 40
E. t= 300-290 /√40 /35+ 35/40
a. A
b. B
c. C
d. D
e. E

Answer: D

Step-by-step explanation:

The test statistic is t = 1.14.

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean  and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean  and standard deviation .

here, we have,

Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean  and standard deviation

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

From a random sample of 35 customers at Store M, the average amount spent was $300 with standard deviation $40.

This means that , μ_m = 6.761

From a random sample of 40 customers at Store V, the average amount spent was $290 with standard deviation $35.

This means that , μ_v = 5.534

Assuming a null hypothesis of no difference in population means

At the null hypothesis, we test that there is no difference, that is, the subtraction of the means is 0. So

H₀ = 0

At the alternate hypothesis, we test if there is difference, that is, the subtraction of the means is different of 0. So

H₁ ≠ 0

The test statistic is:

t = X - μ / s

In which X is the sample mean,  is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that μ= 0

From the samples:

X = 10

s = 8.737

The test statistic is t = 1.14.

To learn more on Central Limit Theorem:

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Complete question:

A two-sample t-test for a difference in means will be conducted to investigate whether the average amount of money spent per customer at Department Store M is different from that at Department Store V. From a random sample of 35 customers at Store M, the average amount spent was $300 with standard deviation $40. From a random sample of 40 customers at Store V, the average amount spent was $290 with standard deviation $35. Assuming a null hypothesis of no difference in population means, what is the test statistic for the appropriate test to investigate whether there is a difference in population means?

The sum of two numbers is 44. One number is 3 times as large as the other. What are the numbers?
Larger number:
0
Smaller number: 0
Х
5
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Exp
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