# 3 In a time use study 25 randomly selected managers were found to spend a mean time of 2.4 hours per day on paperwork with a standard deviation of 1.30 hours. Construct a 98% confidence interval for μ, the mean time spent on paperwork by all managers.
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- The breaking strengths of cables produced by a certain manufacturer have a mean, u, of 1875 pounds, and a standard deviation of 100 pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, 50 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1912 pounds. Can we support, at the 0.1 level of significance, the claim that the mean breaking strength has increased? (Assume that the standard deviation has not changed.) Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H,. p H, :0 H, :0 (b) Determine the type of test statistic to use. (Choose one) ▼ D=0 OSO O20 (c) Find the value of the test statistic. (Round to three or more decimal…A new computer chip design(A) is being compared to the current design(B).Fifty independent chips of each design are tested for speed at performing a certain task. The new computer chip (A) performed the task in 481.2 ms, on average, with a sample standard deviation of 14.3 ms. The current computer chip (B) performed the task in 495.6 ms, on average, with a sample standard deviation of 16.4 ms. Can you conclude, at a 5% significance level, that chip A performs this task faster than chip B?7.44 Facebook use in college. Because of Facebook's popularity among college students, there is a great deal of interest in the relationship between Facebook use and academic performance. One study collected information on n=1839 undergraduate students to look at the relationships among frequency of Facebook use, participation in Facebook activities, time spent preparing for class, and overall GPA.34 Students reported preparing for class an average of 706 minutes per week, with a standard deviation of 526 minutes. Students also reported spending an average of 106 minutes per day on Facebook, with a standard deviation of 93 minutes; 8% of the students reported spending no time on Facebook. (a) Construct a 95% confidence interval for the average number of minutes per week a student prepares for class. (b) Construct a 95% confidence interval for the average number of minutes per week a student spends on Facebook. (Hint: Be sure to convert from minutes per day to minutes per week.) (c)…
- Hoaglin, Mosteller, and Tukey (1983) presented data on blood levels of beta-endorphin as a function of stress. They took beta-endorphin levels for 19 patients 12 hours before surgery and again 10 minutes before surgery. The data are presented below, in fmol/ml Construct a 95% confidence limits on the true mean difference between endorphin levels at the two times described. Participant 12 hours before 10 minutes before 1 10 6.5 2 6.5 14.0 3 8.0 13.5 4 12 18 5 5.0 14.5 6 11.5 9.0 7 5.0 18.0 8…Construct a 95% confidence interval for the true average number of visitors per day to ashopping mall if it was found that on 30 randomly selected days, the average number of visitors per day was 100.25, with a standard deviation of 7.5. Interpret your answer.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
- Suppose a brewery has a filling machine that fills 12-ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 12.27 ounces and a standard deviation of 0.04 ounce. The company is interested in reducing the amount of extra beer that is poured into the 12 ounce bottles. The company is seeking to identify the highest 1.5% of the fill amounts poured by this machine. For what fill amount are they searching? Round to the nearest thousandth. 12.357 oz O 11.913 oz O 12.183 oz 12.087 oz O 306Researchers interested in determining the relative effectiveness of two different drug treatments on people with a chronic illness established two independent test groups. The first group consisted of 12 people with the illness, and the second group consisted of 14 people with the illness. The first group received treatment 1 and had a mean time until remission of 166 days with a standard deviation of 8 days. The second group received treatment 2 and had a mean time until remission of 163 days with a standard deviation of 9 days. Assume that the populations of times until remission for each of the two treatments are normally distributed with equal variance. Construct a 90% confidence interval for the difference −μ1μ2 between the mean number of days before remission after treatment 1 ( μ1 ) and the mean number of days before remission after treatment 2 ( μ2 ). Then find the lower limit and upper limit of the 90% confidence interval. Carry your intermediate…2. A common claim is that garlic lowers cholesterol levels. In a test of the effectiveness of garlic, 49 subjects were treated with doses of raw garlic, and their cholesterol levels were measured before and after the treatment. The changes in their levels of LDL cholesterol have a mean of 0.4 and a standard deviation of 21. Use the sample n = 49 to construct a 95% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. n=49₁ x=0,4₁ 5=21₁ CL = 95%, df=n-1 df=49-1=48
- Researchers interested in determining the relative effectiveness of two different drug treatments on people with a chronic illness established two independent test groups. The first group consisted of 15 people with the illness, and the second group consisted of 11 people with the illness. The first group received treatment 1 and had a mean time until remission of 187 days with a standard deviation of 6 days. The second group received treatment 2 and had a mean time until remission of 162 days with a standard deviation of 8 days. Assume that the populations of times until remission for each of the two treatments are normally distributed with equal variance. Construct a 90% confidence interval for the difference H₁-H₂ between the mean number of days before remission after treatment 1 (H₁) and the mean number of days before remission after treatment 2 (H₂). Then find the lower limit and upper limit of the 90% confidence interval. Carry your intermediate computations to at least three…A sports news station wanted to know whether people who live in the North or the South are bigger sports fans. For its study, 121 randomly selected Southerners were surveyed and found to watch a mean of 4.6 hours of sports per week. In the North, 176 randomly selected people were surveyed and found to watch a mean of 3.2 hours of sports per week. Find a 90% confidence interval for the true difference between the mean numbers of hours of sports watched per week for the two regions if the South has a population standard deviation of 1.6 hours per week and the North has a population standard deviation of 1.4 hours per week. Let Population 1 be people who live in the South and Population 2 be people who live in the North. Round the endpoints of the interval to one decimal place, if necessary. Lower endpoint: Upper endpoint:in a test of the effectiveness of garlic for lowering cholesterol, 43 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes in their levels of LDL cholesterol have a mean of 5.7 and a standard deviation of 17.7. Construct a 99% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic and reducing LDL cholesterol?
