The following data sets represent simple random samples from a population whose

Question

The following data sets represent simple random samples from a population whose mean is 100. Complete parts (a) through (e) below. (b) For each data set, construct a 95% confidence interval about the population mean. CD A 95% confidence interval for data set 1 is (Use ascending order. Round to two decimal places as needed.) Full data set Data SetI 106 125 89 124 87 72 79 107 Data' Selll A 95% confidence interval for data set 11 is ( ). 106 125 89 124 87 72 79 107 (Use ascending order. Round to two decimal places as 88 86 1 86 114 117 97 120 needed.) 96 85 82 102 Data'Setm_ - - A 95% confidence interval for data set lll is ( 106 125 89 124 87 72 79 107 (Use ascending order. Round to two decimal places as 88 86 111 86 114 117 97 120needed.) 96 85 82 102 88 108 115 93 102 78 84 108 94 115 (c) What impact does the sample size n have on the width of the interval? A. As the sample size increases, the width of the O B. The sample size has no impact on the width of O C. As the sample size increases, the width of the (d) Suppose that the data value 106 was accidentally the interval. interval increases. recorded as 061 . For each data set, construct a 95% Click to select your answerls).

Explanation / Answer

Here we have given three datasets of which we have to find confidence interval.

95% confidence interval for population mean (mu) is,

Xbar - E < mu < Xbar + E

where Xbar is sample mean.

E is margin of error.

E = tc * (s / sqrt(n))

s is standard deviation of sample.

n is sample size.

b) Data set 1 :

Summary statistics is,

Variable N Mean StDev SE Mean 95% CI   
data1 8 98.63 19.95 7.05 (81.95, 115.30)  
data2 20 98.65 16.03 3.59 (91.15, 106.15)  
data3 30 98.60 14.87 2.72 (93.05, 104.15)

For 95% confidence level tc= 2.36

E = 2.36 * (19.95 / sqrt(8)) = 16.68

lower llimit = Xbar - E = 98.625 - 16.68 = 81.95

upper limit = Xbar + E = 98.625 + 16.68 = 115.30

95% confidence interval for mu is (81.95, 115.30)

Similarly for data set2 :

95% confidence interval for mu is (91.15, 106.15)

For data set 3 :

95% confidence interval for mu is (93.05, 104.15)

As sample size increases the width of the confidence interval decreases.

Now in the d) part we have to change observation 106 to 061 and reconstruct confidence interval.

The summary statistics is,

Variable N Mean StDev SE Mean 95% CI   
data1 8 93.00 23.59 8.34 (73.28, 112.72)  
data2 20 96.40 17.99 4.02 (87.98, 104.82)
data3 30 97.10 16.30 2.98 (91.01, 103.19)

95% confidence interval for data set 1 is (73.28, 112.72)

95% confidence interval for data set 2 is (87.98, 104.82)

95% confidence interval for data set 3 is (91.01, 103.19)

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