Please note that this question consists of six parts. You may use MINITAB to find a final answer. However you MUST show all the mathematical work to get to the final answer. Just giving the answer without adequate work/explanation may result in zero for the question.  A university wants to compare the proportion of graduate students and undergraduate students who had an internship last summer. A random sample of 200 undergraduate students and 85 graduate students was surveyed. Among the 200 undergraduate students, 102 reported having an internship. And among the 85 graduate students, 50 reported having an internship. Give a point estimate for the difference in population proportions of undergraduate and graduate students who had an internship.  Set up appropriate null and alternative hypothesis for testing if the population proportion of undergraduate students who had an internship is lower than the population proportion of graduate students who had an internship.  What conditions need to be satisfied in order for you to continue with the hypothesis test in part 2? Are they satisfied? Calculate the test statistic for the test you set up in part 2. You may use MINITAB to get the final test statistic. However, you need to show the mathematical calculation that resulted in the final answer. Give the rejection region for this problem. Use 5% significance level. Write the final conclusion in the context of the problem.

Please note that this question consists of three parts. You may use MINITAB to find a final answer. However you MUST show all the mathematical work to get to the final answer. Just giving the answer without adequate work/explanation may result in zero for the question.  A local manufacturing company produces light bulbs. The lifespan of their light bulbs is normally distributed with mean 1160 hours and standard deviation 105 hours.  What is the probability that the lifespan of a randomly selected light bulb manufactured by the company will be over 1200 hours? What value divides the longest 1% lifespans from the rest 99% of lifespans?  A quality control team randomly selects a sample of 40 light bulbs and measures their lifespans. What is the probability that the average lifespan of 40 light bulbs will be over 1200 hours?

Here are tables you may need for this exam. (Click on the file name, not the downarrow to open the table within the spacer) Z_T_CHITables.pdf

Please note that this question consists of six parts. You may use MINITAB to find a final answer. However you MUST show all the mathematical work to get to the final answer. Just giving the answer without adequate work/explanation may result in zero for the question.  A company wants to know if the office location affects productivity. Management randomly select employees from each of four different office locations and record the number of tasks completed in a day. They decided to use One-way ANOVA and need your help to interpret the results. Use provided partial output to answer below questions.  Write down the null and alternative hypotheses for testing whether or not the average number of tasks completed per day is the same for the four locations. Define parameters when you set up null and alternative hypotheses. Compute the degrees of freedom missing in the ANOVA output (i.e. error degrees of freedom) Compute the sum of squares missing in the table (i.e. sum of square treatment) Compute the F-value missing in the ANOVA output. At a 5% significant level is there sufficient evidence to claim that the the average number of tasks completed per day is different in at least one of the locations. Explain your answer. The output for Tukey pairwise comparisons is given below. Based on the output: Are the average number of tasks completed per day for locations 1 and 4 significantly different? Explain your answer. Which location seems to have the highest average number of tasks completed per day?

Random samples of graduate and undergraduate Penn State students were asked about the amount of time they play video games in a typical week. The researcher who gathered the data thinks that the average time spend playing video games in a typical week will be different for graduate and undergraduate students. The correct null hypothesis and alternative hypothesis to answer the researcher’s question would be: 

For the test of whether the true mean monthly rent for Penn State graduate students is greater than $1000,  

Please note that this question consists of five parts. You may use MINITAB to find a final answer. However you MUST show all the mathematical work to get to the final answer. Just giving the answer without adequate work/explanation may result in zero for the question.  A cookie company claims that more than 60% of the cookies in their mixed cookie boxes are chocolate chip. A customer suspects this might not be true. To test the customer’s question, a box of cookies was randomly selected and the number of chocolate chip cookies was counted. Out of 70 cookies, 38 turn out to be chocolate chip. Set up appropriate null and alternative hypotheses that answers customer’s question. Are the conditions to carry out the above test satisfied? Show your work for checking the conditions rather simple “yes” or “no” answer. Calculate the test statistic (show the mathematical work) Calculate the p value for the test. You may use MINITAB to find the numerical value of the p value for the test. However, you MUST clearly write down the probability statement Write the final conclusion in the context of the problem (use 5% significance level). 

For each statement about hypothesis testing for the population mean, state if it is true or false. 

T distribution is symmetric around 0. This is a statement. For a t distributed random variable T,  

The administration of a large university is planing on increasing the student fees with the intention of using majority of the funds towards renovations in the football stadium. In a random sample of 60 students, 38 support of the idea. A 90% confidence interval for the true proportion of students who oppose this idea is