Question

A pharma company claims that there are at least 90 g of cream in every jar. You decide to test the claim at a significance level (alpha) of .05. You randomly sample 25 jars of cream made by the company and find the sample mean to be 92.5 g with a sample standard deviation of 5.5 g.

(a) What are the null and alternate hypotheses?

(b) Draw the picture of the distribution of the test statistic (under H0). Include critical value(s) and region(s) of rejection.

(c) What is the calculated (computed) value of the test statistic? (d) What is your conclusion?

Answer 1

x̅ = 92.5, s = 5.5, n = 25

a)

Null and Alternative hypothesis:

Ho : µ ≥ 90

H1 : µ < 90

b)

df = n-1 = 24

Critical value :

Left tailed critical value, t-crit = T.INV(0.05, 24) = -1.711

Reject Ho if t < -1.711

c)

Test statistic:

t = (x̅- µ)/(s/√n) = (92.5 - 90)/(5.5/√25) = 2.2727

d)

Decision:

t = 2.27 > -1.711, Do not reject the null hypothesis

Conclusion:

There is not enough evidence to reject the null hypothesis that there are at least 90 g of cream in every jar at 0.05 significance level.