Lesson 8: Hypothesis Testing NAME Lab Activity Answer the following questions showing all work. For questions that require Minitab Express, include the appropriate output (copy + paste) along with an explanation. 1. For the following scenarios, write the appropriate null and alternative hypotheses. Use the appropriate symbols (Ho, Ha, , p). A. The University wants to know if, on average, World Campus students are enrolled in more than 9 credits this semester. B. World Campus wants to know if more than 50% of students plan to enroll in courses this summer. C. An article reports that the majority of people lose weight on a certain diet. You want to provide evidence that the article is wrong. D. Is the mean age of University Park freshman less than 20 years? E. Do students at State College Area High School do better than the national average of 500 on the Verbal section of the SAT? Lesson 8: Hypothesis Testing NAME Lab Activity 2. Answer the following questions using the dataset SP16STUDENTDATA.MTW Consider this data to be a sample that is representative of the population of all Penn State World Campus STAT 200 students. Please use Minitab/Minitab Express for this question as needed. A. At the .01 alpha level, is there evidence that the proportion of all World Campus STAT200 students who are dieting is different from 30%? Use the five-step hypothesis testing procedure. The sample size is 520. B. At the .01 alpha level, is there evidence that more than 30% of Penn State World Campus STAT 200 students have a cat? Use the five-step hypothesis testing procedure. Lesson 8: Hypothesis Testing NAME Lab Activity C. Construct a 95% confidence interval for the population mean of the variable ideal marriage age. Assume that in the population this variable is normally distributed. D. Is there evidence that the mean ideal marriage age is different from 28? E. At the .05 alpha level, is there evidence that the mean ideal marriage age is different from 28? Assume that in the population this variable is normally distributed. Use the five-step hypothesis testing procedure. Lesson 8: Hypothesis Testing NAME Lab Activity F. Compare your results from part (D) and part (E). Do they match to each other? G. In terms of the scenario in part (E), explain each of the following changes would impact power: Increase in sample size Change in alpha from .05 to .15 3. A test prep company has developed a new intervention to improve SAT-Math scores. They will conduct a hypothesis test to determine if the average SATMath score of a student who has completed their program is greater than the known national average of 500. The program is very expensive ($2,800 per student). Use this scenario to answer the following questions. A. Write out the null and alternative hypotheses using the appropriate symbols. B. In terms of this scenario, what would a Type I error be? C. In terms of this scenario, what would a Type II error be? D. The researchers used a sample size of n= 10,500 and found a sample mean of 504. Using your hypotheses from part (A) and the known population standard deviation of 100, what is the t test statistic? Please compute it by hand using the formula. E. What is the p-value associated with the test statistic you computed in part (D)? Please use t table or the software. Lesson 8: Hypothesis Testing NAME Lab Activity F. Are the results of this study statistically significant at the .05 alpha level? Why or why not. G. Are the results of this study practically significant? For example, if you were a parent, would you be convinced that you should spend $2,800 to send your child through this program? Explain why