Bao conducts a research study on a random sample of 60 Harvard undergraduate students to determine the average number of books that they purchase for the 2021-2022 academic year. Based on surveys that were administered in prior years, Bao believes that the standard deviation of books in the population of all Harvard undergrads is 7.

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 7.1 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 6.1, 8.1, 9.1, 10.1, 7.1, 11.1, and 12.1 pounds. What is the sample standard deviation?

Suppose that El Camino is studying the average number of hours students study for classes per week. According to research from 2010 El Camino students spent an average of 21 hours a week studying for classes. El Camino wants to study if this average has changed. To do this they take a random sample of 81 current students and find that the average student spent 19.3 hours studying with a standard deviation of 6.4 hours. (Note: You may assume there are approximately 20,000 El Camino students). (a) Carry out a hypothesis test at α = .05 to test the claim that the average number of hours per week that El Camino students study has changed since 2010. (b) Describe what it would mean in this situation to make a Type I error (c) Describe what it would mean in this situation to make a Type II error (d) Construct a 95% confidence interval for the average number of hours studied by El Camino students per week. Make sure to interpret your interval.

A professor believes the class he is teaching in the current semester is below the average of the classes he has taught. In order to test this hypothesis, he analyses the scores of midterm of all 100 students he teaches this semester. Their average score of this exam is 79 out of 100, with a standard deviation of 12. The mean score of the midterm for all students that he has taught for the last thirty-two years is 83 out of 100, with a standard deviation of 14. Use an alpha level of 0.01 for this analysis.  Part B.State the null hypothesis and the alternative hypothesis:

Scientists collect a simple random sample of 25 menthol cigarettes and 25 non-menthol cigarettes. Both samples consist of cigarettes that are filtered, 100mm long, and non-light. The menthol cigarettes have a mean nicotine amount of 0.87 mg and a standard deviation of 0.24 mg. The non-menthol cigarettes have a mean nicotine amount of 0.92 mg and a standard deviation of 0.25 mg. Use a 0.05 significance level to test the claim that non-menthol cigarettes have greater amounts of nicotine than menthol cigarettes. Assume population variances are not equal.

One year, the distribution of salaries for professional sports players had a mean of $1.6 million and a standard deviation of $0.7 million. Suppose a sample of 100 major league players was taken. Find the approximate probability that the average salary of the 100 players that year exceeds $1.1 million.

Nationally, the population as a whole watches 6.2 hours of TV per day. A random sample of 1,017 senior citizens report watching an average of 4.6 hours of TV daily, with a standard deviation of 0.7. Which test do we use to determine if senior citizens watch a statistically significant lower amount of TV? Why? Should it be one or two tailed?

A successful basketball player has a height of 6 feet 11 ​inches, or 211 cm. Based on statistics from a data​ set, his height converts to the z score of 5.17. How many standard deviations is his height above the​ mean?

King Tut was an ancient Egyptian ruler whose tomb was discovered and opened in 1923 . Legend has it that the archaeologists who opened the tomb were subject to a "mummy's curse," which would shorten their life spans. A team of scientists conducted an investigation of the mummy's curse. They reported that the 24 people exposed to the curse had a mean life span of 71.1 years with a standard deviation of 11.6 years, while a sample of 12 Westerners in Egypt at the time who were not exposed to the curse had a mean life span of 77.7 years with a standard deviation of 13.9 years. Assume that the populations are approximately normal. Can you conclude that the mean life span of those exposed to the mummy's curse differs from the mean life span of those not exposed? Let μ1 denote the mean life span of those exposed to the mummy's curse and μ2 denote the mean life span of those not exposed. Use the =α0.01 level and the P -value method with the TI-84 Plus calculator. do we…

A professor believes the class he is teaching in the current semester is below the average of the classes he has taught. In order to test this hypothesis, he analyses the scores of midterm of all 100 students he teaches this semester. Their average score of this exam is 79 out of 100, with a standard deviation of 12. The mean score of the midterm for all students that he has taught for the last thirty-two years is 83 out of 100, with a standard deviation of 14. Use an alpha level of 0.01 for this analysis.    Part C. Find the critical value: