Recent publications have hinted at the growing importance of sleep in the elderly in order to maintain good health. Suppose a researcher is interested in the hypothesis that the difference in average hours of sleep differs significantly between men aged 35-45 and men aged 45+.Assume the following table summarizes the descriptive statistics for SRSs from each age group.Carry out the appropriate statistical test to answer the researcher’shypothesis regarding the difference in average hours of sleep between the two groups under investigation. Assume that all conditions for the testing are met. Use an alpha level of 0.05. Calculate a pooled variance under the equal variance assumption. Write out your null and alternative hypotheses and interpret your pvalue. Age group Average hours of sleep Standard deviation Sample size 35-45 7.4 1.02 24 45+ 5.2 0.87 32

Citrus Rental is a popular car rental agency that has a history of having too few cars available, so that its available cars are overdriven. The mean monthly mileage over the years for Citrus cars has been about 1500 miles per month. Recently, though, Citrus purchased thousands of new cars, and the company claims that the average mileage of its cars is now less than in the past. To test this, a random sample of 11 recent mileages of Citrus cars was taken. The mean of these 11 mileages was 1332 miles per month, and the standard deviation was 232 miles per month. Assume that the population of recent monthly mileages of Citrus cars is normally distributed. At the 0.05 level of significance, can it be concluded that the mean recent monthly mileage, u, of Citrus cars is less than 1500 miles per month? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary,…

Is narcissism a more common personality trait today than it was a few decades ago?  It is known that the mean population score on the Narcissistic Personality Inventory (NPI) for students attending University of South Alabama around 20 years ago was μ= 15 (Twenge, 2010).  Interested in the narcissism levels of students in the year 2020, a researcher administers the NPI to a random sample of 25 University of Alabama sophomores this Spring term. The mean NPI score from the researcher’s sample of sophomores is M = 16.5, with s = 3.4. 1. Write the null and alternative hypotheses in symbols. Possible symbols for your answer: H0, H1, μ, M, σ. 2. Calculate the standard error.  3. Find the critical value for the test statistic, assuming alpha = .05 (Use largest [i.e., most conservative] value if exact value not given in the chart)  a) 2.064 b) 1.96 c) 1.98 d) 2.000

Citrus Rental is a popular car rental agency that has a history of having too few cars available, so that its available cars are overdriven. The mean monthly mileage over the years for Citrus cars has been about 1550 miles per month. Recently, though, Citrus purchased thousands of new cars, and the company claims that the average mileage of its cars is now less than in the past. To test this, a random sample of 13 recent mileages of Citrus cars was taken. The mean of these 13 mileages was 1425 miles per month, and the standard deviation was 209 miles per month. Assume that the population of recent monthly mileages of Citrus cars is normally distributed. At the 0.10 level of significance, can it be concluded that the mean recent monthly mileage, μ, of Citrus cars is less than 1550 miles per month? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary,…

1. Are there any statistically significant differences between the patients assigned to the experimental treatment and placebo? Justify 2.  Consider the comparison of treatments with respect to patient age. Run appropriate test using data.

Citrus Rental is a popular car rental agency that has a history of having too few cars available, so that its available cars are overdriven. The mean monthly mileage over the years for Citrus cars has been about 1600 miles per month. Recently, though, Citrus purchased thousands of new cars, and the company claims that the average mileage of its cars is now less than in the past. To test this, a random sample of 16 recent mileages of Citrus cars was taken. The mean of these 16 mileages was 1517 miles per month, and the standard deviation was 233 miles per month. Assume that the population of recent monthly mileages of Citrus cars is normally distributed. At the 0.05 level of significance, can it be concluded that the mean recent monthly mileage, μ, of Citrus cars is less than 1600 miles per month? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary,…

Smoke-Free Legislation and AsthmaHospital admissions for asthma in children younger than 15 years was studied1 in Scotland both before and after comprehensive smoke-free legislation was passed in March 2006. Monthly records were kept of the annualized percent change in asthma admissions, both before and after the legislation was passed. For the sample studied, before the legislation, admissions for asthma were increasing at a mean rate of 5.2% per year. The standard error for this estimate is 0.7% per year. After the legislation, admissions were decreasing at a mean rate of 18.2% per year, with a standard error for this mean of 1.79%. In both cases, the sample size is large enough to use a normal distribution.1Mackay, D., et. al., ‘‘Smoke-free Legislation and Hospitalizations for Childhood Asthma,” The New England Journal of Medicine, September 16, 2010; 363(12):1139-45.   (a) Find a 95% confidence interval for the mean annual percent rate of change in childhood asthma hospital…

What does it mean to be statistically literate?