Activity 3 Hypothesis Tests Obtain the data for this activity on the website When you click the link the data should open up automatically in Minitab 1 The first column of the data gives observations on the breakdown voltage kV for a particular insulating liquid Suppose we want to test whether the mean breakdown voltage for this insulating liquid is more than 53 kV a What are the null and alternative hypotheses b Define the parameter the one in your hypotheses above in words Hint The answer already appears somewhere above on this page c Perform the rest of the steps of the hypothesis test by hand using 05 Do you reject the null hypothesis To obtain the summary statistics that you need go to Stat Basic Statistics Display Descriptive Statistics Enter Breakdown Voltage as the variable Use the summary statistics to perform the hypothesis test Case II in Section 8 2 SHOW YOUR WORK d Now read the following definition the gist of which you should memorize before the next exam The p value is the probability calculated assuming H0 is true of obtaining a test statistic at least as supportive of Ha as the statistic actually observed In this case your Z test statistic should be standard normal assuming H0 is true Therefore because Ha uses you just need to find the probability that a standard normal variable would be greater than your observed z statistic Find this p value by hand explaining your work d Now check your work in Minitab Go to Stat Basic Statistics 1 Sample t Enter Breakdown Voltage as the variable and 53 as the test mean Under Options adjust the alternative to match your answer to part a Copy and paste the p value from Minitab Note This value will not match exactly what you calculated by hand for various reasons but it should be close e Read the alternative definition of p value at the bottom of p 346 How can you tell at a glance by looking at your p value whether to reject H0 using 05 Would you have rejected using 01 Why or why not 2 The second column of the data gives responses to the question Are you a member of a fraternity or sorority The question was answered by a sample of PSU students Assuming this is a random sample of students we want to test whether the percentage of PSU students who are part of the Greek system is different than 20 a What are the appropriate null and alternative hypotheses b Define the parameter the one in your hypotheses above in words Again it s written somewhere above c Perform the rest of the steps of the hypothesis test by hand and obtain a pvalue SHOW YOUR WORK You can obtain the info you need by selecting Stat Tables Tally You should also know that all tests of proportions use Z statistics as long as np0 10 and n 1 p0 10 and that the formula for Z appears on p 340 of the textbook Note in this case that your alternative is 2 tailed which means that your pvalue should be the probability that a standard normal variable is less than the observed z OR greater than z in other words by symmetry you ll need to multiply by two after you use Table A 3 d Now check your work in Minitab Go to Stat Basic Statistics 1 Proportion and enter Greek as the variable Under Options make sure to choose the appropriate alternative and null value Check the box beside Use test and interval based on normal distribution Report the test statistic and p value