Question

A manufacturer claims that each bag of their chocolate covered pretzels contains at least 9 red chocolate covered pretzels. A sample of 25 bags of these pretzels yields an average of 8 red chocolate covered pretzels with a sample standard deviation of 0.7 .Test their claim at a 5% significance level. (State the null and alternative hypotheses. Be sure to clearly state the “rejection region” for the test, and state your conclusion in words.)

Answer 1

Solution:

This is a left (One) tailed test,

The null and alternative hypothesis is,  

Ho: 9

Ha: 9

The test statistics,

t =( - )/ (s /n)

= ( 8 - 9 ) /( 0.7 / 25 )

= -7.143

Critical value of  the significance level is α = 0.05, and the critical value for a two-tailed test is

= -1.711

Reject H0. if t < -1.711

Since it is observed that t = -7.143 < = -1.711, it is then concluded that the null hypothesis is rejected.

P-value = 0.000

The p-value is p = 0 < 0.05, it is concluded that the null hypothesis is rejected.

There is sufficient evidence to claims that each bag of their chocolate covered pretzels contains at least 9 red chocolate covered pretzels.