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Constructing Confidence Intervals In Exercises 45 and 46, use the information to construct 90% and 99%...

Constructing Confidence Intervals In Exercises 45 and 46, use the information to construct 90% and 99% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals.

45. DVR and Other Time-Shifted Viewing A group of researchers estimates the mean length of time (in minutes) the average U.S. adult spends watching television using digital video recorders (DVRs) and other forms of time-shifted television each day. To do so, the group takes a random sample of 30 U.S. adults and obtains the times (in minutes) below.

29 12 23 24 33 24 28 31 18 27 27 32 17 13 17 12 21 32 26 16 28 28 21 24 29 13 20 13 21 27

From past studies, the research council assumes that s is 6.5 minutes. (Adapted from the Nielsen Company)

46. Sodium Chloride Concentrations The sodium chloride concentrations (in grams per liter) for 36 randomly selected seawater samples are listed. Assume that s is 7.61 grams per liter.

30.63 33.47 26.76 15.23 13.21 10.57 16.57 27.32 27.06 15.07 28.98 34.66 10.22 22.43 17.33 28.40 35.70 14.09 11.77 33.60 27.09 26.78 22.39 30.35 11.83 13.05 22.22 13.45 18.86 24.92 32.86 31.10 18.84 10.86 15.69 22.35

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Expert Solution

45) = (29 + 12 + 23 + 24 + 33 + 24 + 28 + 31 + 18 + 27 + 27 + 32 + 17 + 13 + 17 + 12 + 21 + 32 + 26 + 16 + 28 + 28 + 21 + 24 + 29 + 13 + 20 + 13 + 21 + 27)/30 = 22.87

At 90% confidence level, the critical value is z0.05 = 1.645

The 90% confidence interval is

b) At 99% confidence level, the critical value is z0.005 = 2.58

The 99% confidence interval is

46)a) = (30.63 + 33.47 + 26.76 + 15.23 + 13.21 + 10.57 + 16.57 + 27.32 + 27.06 + 15.07 + 28.98 + 34.66 + 10.22 + 22.43 + 17.33 + 28.4 + 35.7 + 14.09 + 11.77 + 33.6 + 27.09 + 26.78 + 22.39 + 30.35 + 11.83 + 13.05 + 22.22 + 13.45 + 18.86 + 24.92 + 32.86 + 31.10 + 18.84 + 10.86 + 15.69 + 22.35)/36 = 22.10

At 90% confidence level, the critical value is z0.05 = 1.645

The 90% confidence interval is

At 99% confidence level, the critical value is z0.005 = 2.58

The 99% confidence interval is

orchestra answered 1 year ago

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