# Hypothesis testing for mean and proportion, critical value

Inspection of student data generated during pre/post treatment surveys shows that among 10 subjects, 7 had higher scores after an experimental treatment, 2 had lower scores, and 1 score did not change. Using the traditional method of hypothesis testing, we need to determine if the experimental course has any effect. Use an alpha level of .01. If the computed test statistic is 2.36, what is the critical value (2 decimal places of significance, and did the experimental course make a difference (Yes or No))?

Students at the University of Arkansas randomly selected 217 student cars and found that they had ages with a mean of 7.89 years and a standard deviation of 3.67 years. They also randomly selected 152 faculty cars and found that they had ages with a mean of 5.99 years and a standard deviation of 3.65 years. Use a 0.01 significance level to test the claim that student cars are older than faculty cars. What are the critical value (3 places of significance) and t score (2 places of significance)? Are student cars older (Yes or No)?

A U.S. Department of Justice report included the claim that "in spouse murder cases, wife defendants were less likely to be convicted than husband defendants." Sample data consisted of 277 convictions among 318 husband defendants and 155 convictions among 222 wife defendants. Test the stated claim. Assume Aplha = 0.05. What are the Critical value and z score, each to two decimal places of precision? Do you reject the null hypothesis (Yes or No)?

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#### Solution Preview

1. Inspection of student data generated during pre/post treatment surveys shows that among 10 subjects, 7 had higher scores after an experimental treatment, 2 had lower scores, and 1 score did not change. Using the traditional method of hypothesis testing, we need to determine if the experimental course has any effect. Use an alpha level of .01. If the computed test statistic is 2.36, what is the critical value (2 decimal places of significance, and did the experimental course make a difference (Yes or No))?

The degree of freedom is 10-1=9

So the T-value for 0.01 and degree of freedoms of 9 for a two tail test is 3.25

Since critical value is more than the observed value, we failed to reject the null and hence there is no ...

#### Solution Summary

This post answers three questions on hypothesis testing. Could be used as a good practice exercise.