10 11 12 13 14 15 16 17 18 19 20 Critical alue 2.228 2.201 2.179 2.160 2.145 2.1

Question

10 11 12 13 14 15 16 17 18 19 20 Critical alue 2.228 2.201 2.179 2.160 2.145 2.131 2.120 2.110 2.101 2.093 2.086 2.080 16. The students in a statistics class collected a random sample of twenty brands of chocolate ice cream. The numbers of calories, per half-cup serving, are given below. (As a check of your data entry, the mean is 166.) (10 pts) 220 130 130 150 170 140 160 160 190 190 170 150 110 180 170 90 240 250 220 100 Construct a 95% confidence interval for the population mean calories in a half cup of chocolate ice cream. You may use the table of critical t values above. Although you may check your results with your calculator (TInterval), show your computations. That is, show the calculation for the margin of error E, stating the critical t value that you use, and the calculation for the confidence interval lower and upper limits. Use the reference page, as needed. However, please use your calculator to compute the mean and standard deviation of the sample.) Explain what your 95% confidence interval means about the calories per half-cup serving of ice cream.

Explanation / Answer

mean =166 , std.deviation = 42.9418 , n= 20

t value at 95% = 2.093

Margin of error = t *(s/sqrt(n))
= 2.093 *(42.9418/sqrt(20))
= 20.0972

CI = mean +/- t *(s/sqrt(n))
= 166 +/- 2.093 *(42.9418/sqrt(20))
= (145.9028,188.8447)

Lower limit = 145.9028
Upper limit = 188.8447

There is 95% confidence interval means about the calories per half cup serving ice cream is between 145.9028 and 188.8447

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