a test of sobriety involves measuring the subject's motor skills. twenty randomly selected sober subjects take the test and produce a mean score of 41.0 with a standard deviation of 3.7. at the 0.01 level of significance, test the claim that the true mean score for all sober subjects is equal to 35.0. use the traditional method of testing hypotheses.

Answer:

Since the pvalue of the test is 0 < 0.01, we reject the null hypothesis and accept the alternate hypothesis that the true mean score for all sober subjects is different of 35.

Step-by-step explanation:

Test the claim that the true mean score for all sober subjects is equal to 35.0.

This means that the null hypothesis is:

[tex]H_{0}: \mu = 35[/tex]

And the alternate hypothesis is:

[tex]H_{a}: \mu \neq 35[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

35 is tested at the null hypothesis:

This means that [tex]\mu = 35[/tex]

Sample of 20, mean score of 41.0 with a standard deviation of 3.7.

This means that [tex]n = 20, X = 41, \sigma = 3.7[/tex]

Value of test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{41 - 35}{\frac{3.7}{\sqrt{20}}}[/tex]

[tex]z = 7.25[/tex]

Pvalue of the test:

The pvalue of the test is the probability that differs from the mean by at least 41 - 35 = 6, which is the probability that |z| < 7.25.

z = -7.25 has a pvalue of 0

2*0 = 0

Since the pvalue of the test is 0 < 0.01, we reject the null hypothesis and accept the alternate hypothesis that the true mean score for all sober subjects is different of 35.

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Hypothesis Testing is the use of statistics to determine the probability that a given claim is true. In Part II of this project, you will choose a data set, review claims and perform hypothesis testing and make a decision. You will then complete a write-up that includes the calculations. The government logs the number of documented births, deaths, marriages and divorces; however, it is possible to have undocumented cases. In part II of this project, you are going to test claims about total births, deaths, marriages and divorces. Deliverables Choose a Data Set. Go to https://www.cdc.gov/nchs/products/nvsr.htm (Links to an external site.) In the search bar type: Births, Marriages, Divorces, and Deaths screenshot of CDC website toolbar Pick a DataSet and download the PDF document and make note of the volume, number, and date. For example you could use the National Vital Statistics Reports, screenshot of National Vital Statistics Reports webpage Pick the same month/year combination for each data set. For example, choosing September of 2009. screenshot of example dataset Preliminary Calculations Create a summary table for 1. Live Births, 2. Deaths, 3. Marriages, and 4. Divorces highlighting the mean, median, sample standard deviation, minimum and maximum values for each the data sets. You will have FOUR tables using the list of values of each state, the District of Columbia and Puerto Rico (You will have 52 numbers for each data set). Summary Table for _________ Mean Median Standard Deviation Minimum Maximum Hypothesis Testing With the information that you gather from the summary tables, test the following (you can use excel when appropriate): Determine if there is sufficient evidence to conclude the average amount of births is over 5000 in the United States and territories at the 0.05 level of significance. Determine if there is sufficient evidence to conclude the average amount of deaths is equal to 6000 in the United States and territories at the 0.10 level of significance. Determine if there is sufficient evidence to conclude the average amount of marriages is greater or equal to 2500 in the United States and territories at the .05 level of significance. Determine if there is sufficient evidence to conclude the average amount of divorces is less than or equal to 4000 in the United States and territories at the 0.10 level of significance. For each of the tests above, in your report, be sure to— Clearly state a null and alternative hypothesis Give the value of the test statistic Report the P-Value Clearly state your conclusion (Reject the Null or Fail to Reject the Null) Explain what your conclusion means in context of the data. Lastly, propose and conduct your own test of hypothesis about the Birth, Death, Marriage and Divorce data that you have been analyzing. Make sure to follow the five steps above.

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