Question

A company that makes cola drinks states that the mean caffeine content per​ 12-ounce bottle of cola is 55 milligrams. You want to test this claim. During your​ tests, you find that a random sample of thirty​ 12-ounce bottles of cola has a mean caffeine content of 53.4 milligrams. Assume the population is normally distributed and the population standard deviation is 7.2 milligrams. At alphaequals0.02​, can you reject the​ company's claim? Complete parts​ (a) through​ (e). ​(a) Identify Upper H 0 and Upper H Subscript a. Choose the correct answer below. A. Upper H 0​: muless than or equals55 Upper H Subscript a​: mugreater than55 B. Upper H 0​: muequals55 Upper H Subscript a​: munot equals55 C. Upper H 0​: muequals53.4 Upper H Subscript a​: munot equals53.4 D. Upper H 0​: munot equals53.4 Upper H Subscript a​: muequals53.4 E. Upper H 0​: muless than or equals53.4 Upper H Subscript a​: mugreater than53.4 F. Upper H 0​: munot equals55 Upper H Subscript a​: muequals55 ​(b) Find the critical​ value(s). Select the correct choice below and fill in the answer box within your choice. ​(Round to two decimal places as​ needed.) A. The critical value is nothing. B. The critical values are plus or minus nothing. Identify the rejection​ region(s). Choose the correct answer below. A. -4 0 4 z Reject Upper H 0 .Reject Upper H 0 .Fail to reject Upper H 0 . A normal curve is over a horizontal axis labeled z from negative 4 to 4 in increments of 1 and is centered on 0. Vertical line segments extend to the left of and to the right 0 from the horizontal axis to the curve. The area under the curve the left of the left line segment and to the right of the right lines segment is shaded and labeled Reject H@Sub{0}. The area between the vertical line segments is labeled Fail to reject H@Sub{0}. B. -4 0 4 z Reject Upper H 0 .Fail to reject Upper H 0 . A normal curve is over a horizontal axis labeled z from negative 4 to 4 in increments of 1 and is centered on 0. Vertical line segment extends to the right of 0 from the horizontal axis to the curve. The area under the curve to the right of the line segment is shaded and labeled Reject H@Sub{0}. The area under the curve to the left of the line segment is labeled Fail to reject H@Sub{0}. C. -4 0 4 z Reject Upper H 0 .Fail to reject Upper H 0 . A normal curve is over a horizontal axis labeled z from negative 4 to 4 in increments of 1 and is centered on 0. Vertical line segment extends to the left of 0 from the horizontal axis to the curve. The area under the curve to the left of the line segment is shaded and labeled Reject H@Sub{0}. The area under the curve to the right of the line segment is labeled Fail to reject H@Sub{0}. ​(c) Find the standardized test statistic. zequals nothing ​(Round to two decimal places as​ needed.) ​(d) Decide whether to reject or fail to reject the null hypothesis. A. Since z is not in the rejection​ region, reject the null hypothesis. B. Since z is in the rejection​ region, reject the null hypothesis. C. Since z is in the rejection​ region, fail to reject the null hypothesis. D. Since z is not in the rejection​ region, fail to reject the null hypothesis. ​(e) Interpret the decision in the context of the original claim. At the 2​% significance​ level, there ▼ is is not enough evidence to ▼ support reject the​ company's claim that the mean caffeine content per​ 12-ounce bottle of cola ▼ is equal to is greater than is less than is different from nothing milligra

Answer 1

a)

Ho: µ= 55 (claim)
Ha: µ ≠ 55

b)

Critical values at 0.2 level for 29 df is 2.1503

c)

Rejection region to reject H0 is Test statistics <-2.1503 Or Test statistics > 2.1503

d)

Test statistics

t =  x - µ/ σ/√ n

= 53.4 - 55 / 7.2 / sqrt(30)

= -1.217

This is test statistics value. -1.217

e)

Do not reject H0​ because the negative test statistic is less than negative critical value.

We conclude at 0.02 level that, we fail to support the claim.

The null hypothesis is not rejected which implies that there is no sufficient evidence at the a = 0.02 level of significance to conclude that the mean caffeine content per 12-ounce bottle of cola is 55 milligrams.