Question

Tea Bag Weight​ (in grams)
5.665.66	5.465.46	5.445.44	5.415.41	5.545.54	5.325.32	5.565.56	5.445.44	5.535.53	5.415.41
5.575.57	5.425.42	5.545.54	5.535.53	5.565.56	5.615.61	5.565.56	5.475.47	5.465.46	5.535.53
5.465.46	5.415.41	5.465.46	5.625.62	5.525.52	5.315.31	5.695.69	5.285.28	5.485.48	5.545.54
5.795.79	5.595.59	5.415.41	5.565.56	5.575.57	5.495.49	5.315.31	5.515.51	5.555.55	5.595.59
5.62	5.45	5.44	5.26	5.545.54	5.625.62	5.495.49	5.585.58	5.685.68	5.345.34

The accompanying table contains data on the​ weight, in​ grams, of a sample of 50 tea bags produced during an​ eight-hour shift. Complete parts​ (a) through​ (d).

a. Is there evidence that the mean amount of tea per bag is different from

5.5

​grams? (Use alphaαequals=0.05.)

Determine the test statistic. ​(Round to two decimal places as​ needed.)

Find the​ p-value. ​(Round to three decimal places as​ needed.)

State the conclusion. Do not reject, does reject Upper H 0. There is insufficient, sufficent evidence to conclude that the mean difference is not equal to 5.5 inches. b.

Construct a 95​% confidence interval estimate of the population mean amount of tea per bag. Interpret this interval. ​(Round to four decimal places as​ needed.)

Interpret the 95​% confidence interval. Choose the correct answer below. A. Reject Upper H 0 because the hypothesized mean is not contained within the confidence interval. B. Do not reject Upper H 0 because the hypothesized mean is contained within the confidence interval. Your answer is correct.C. Reject Upper H 0 because the hypothesized mean is contained within the confidence interval. D. Do not reject Upper H 0 because the hypothesized mean is not contained within the confidence interval.

c. Compare the conclusions reached in​ (a) and​ (b). Choose the correct answer below. A. The confidence interval and hypothesis test both show that there is insufficient evidence that the mean amount of tea per bag is different from 5.5 grams. B. The confidence interval shows insufficient evidence while the hypothesis test shows sufficient evidence that the mean amount of tea per bag is different from 5.5 grams. C. The confidence interval shows sufficient evidence while the hypothesis test shows insufficient evidence that the mean amount of tea per bag is different from 5.5 grams. D. The confidence interval and hypothesis test both show that there is sufficient evidence that the mean amount of tea per bag is different from 5.5 grams.

Answer 1

Following is the output of descriptive statistics:

Descriptive statistics
	Tea bag weight
count	50
mean	5.5036
sample standard deviation	0.1095
sample variance	0.0120
minimum	5.26
maximum	5.79
range	0.53

Conclusion: There is insufficient evidence to conclude that the mean difference is not equal to 5.5 inches.

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(b)

B. Do not reject Upper H 0 because the hypothesized mean is contained within the confidence interval.

(C)

A. The confidence interval and hypothesis test both show that there is insufficient evidence that the mean amount of tea per bag is different from 5.5 grams.