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following data values are a simple random sample from a population
following data values are a simple random sample from a population that is normally distributed, with ssquared=25.0: 47, 43, 33, 42, 34, and 41. Construct and interpret the 95% and 99% confidence intervals for the population mean.
2. For df=25, determine the value of A that corresponds to each of the following probabilities.
a. P(T=A) = 0.025
b. P(T=A) =0.10
c. P(-A = t =A) = 0.99
3. Given the following observations in a simple random sample from a population that is approximately normally distributed, construct and interpret the 90% and 95% confidence intervals for the mean:
67, 79, 71, 98 74, 70 59, 102, 92, 96
4. A consumer magazine has contacted a simple random sample of 33 owners of a certain model of automobile and asked each owner how many defects had to be corrected within the first two months of ownership. The average number of defects was 3.7 with a standard deviation of 1.8 defects.
a. Use the t distribution to construct a 95% confidence interval for µ= the average number of defects for this model.
b. Use the z distribution to construct a 95% confidence interval for µ= the average number of defects for this model
c. given the population standard deviation is not known, which of these two confidence intervals should be used as the interval estimate for µ?
5. An airline has surveyed a simple random sample of air travelers to find out whether they would be interested in paying a higher fare in order to have access to email during their flight. Of the 400 travelers surveyed, 80 said email access would be worth a slight extra cost. Construct a 95% confidence interval for the population proportion of air travelers who are in favor of the airlines email idea.
6. Based on its 1999 survey, student monitor reports that 20% of US college students used the internet for job hunting during the month preceding the survey. Assuming this finding to be based on a simple random sample of 1600 college students, construct and interpret the 90% confidence interval for the population proportion of college students who used the internet for job hunting during this period.
7. A consumer agency has retained an independent testing firm to examine a television manufacturer’s claim that its 25-inch console model consumes just 110 watts of electricity. Based on a preliminary study, the population standard deviation has been estimated as 11.2 watts for these sets. In undertaking a larger study, and using a simple random sample, how many sets must be tested for this firm to be 95% confident that its sample mean does not differ from the actual population mean by more than 3.0 watts?
8. For each of the following pairs of null and alternative hypotheses, determine whether the pair would be appropriate for a hypothesis test. If a pair is deemed inappropriate, explain why.
a. Ho: µ= 10, H1: µ< 10
b. Ho: µ=30, H1: µ? 30
c. Ho: µ> 90, H1: µ= 90
d. Ho: µ= 75, H1 H1 µ= 85
e. Ho: X-bar = 15, H1: X-bar < 15
f. Ho: X-bar = 58, H1: X-bar ? 58
9. For each of following statements, formulate appropriate null and alternative hypotheses. Indicate whether the appropriate test will be one tail or two tail, then sketch a diagram that shows the approximate location of the “rejection region(s) for the test.
a. The average college student spends no more than $300 per semester at the unicersity bookstore.
b. The average adult drinks 1.5 cups of coffee per day
c. The average SAT score for entering freshmen is at least 1200.
d. The average employee put in 3.5 hours of overtime last week
10. For Each of the following tests and z values, determine the p-value for the test.
a. Left tail test and z= -1.62
b. right tail test and z= 1.43
c. two tail test and z= 1.27
11. For a sample of 12 items from a normally distributed population for which the standard deviation is s= 17.0, the sample mean is 230.8. At the 0.05 level of significance, test Ho: µ= 220 versus H1: µ> 220. Determine and interpret the p-value for the test.
12. The Coffee Association has reported the mean daily coffee consumption for U.S residents as 1.65 cups. Assume that a sample of 38 people from a North Carolina city consumed a mean of 1.84 cups of coffee per day, with a standard deviation of 0.85 cups. In a two tail test at the 0.05 level, could the residents of this city be said to be significantly different from there counterparts across the nation?
13. During 2002, college work study students earned a mean of $1252. Assume that a sample consisting of 45 of the work study students at a large university was found to have earned a mean of $1277 during that year, with a standard deviation of $210. Would a one tail test at the 0.05 level suggest the average earnings of this university’s work study students were significantly higher than the national team?
14. For a simple random sample, n=700 and p= 0.6. At the 0.025 level, test Ho: p = 0.60 versus H1: p > 0.60
15. The director of admissions at a large university says that 15% of high school juniors to whom she sends university literature eventually applies for admission. In a sample of 300 persons to whom material were sent, 30 students applied for admission. In a two tail test at the 0.05 level of significance, should we reject the director’s claim?
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