Question

A local bottler in Hawaii wishes to ensure that an average of 24 ounces of passion fruit juice is used to fill each bottle. In order to analyze the accuracy of the bottling process, he takes a random sample of 50 bottles. The mean weight of the passion fruit juice in the sample is 23.69 ounces. Assume that the population standard deviation is 0.87 ounce.

. Calculate the value of the test statistic.

- Find the p-value.

c-1. What is the conclusion at α = 0.01?
  

• Do not reject H₀ since the p-value is less than the significance level.

• Do not reject H₀ since the p-value is greater than the significance level.

• Reject H₀ since the p-value is less than the significance level.

• Reject H₀ since the p-value is greater than the significance level.

Make a recommendation to the bottler.

The accuracy of the bottling process is

a)compromised

b) not compromised

Answer 1

Claim: A local bottler in Hawaii wishes to ensure that an average of 24 ounces of passion fruit juice is used to fill each bottle that is

The null and alternative hypothesis are:

Population standard deviation is known, so the z test statistics will used.

The formula to find the z test statistics is,

Where,

Plug the values in the formula of z test statistics,

The alternative hypothesis contains not equal to sign so the test is two tailed test and the test statistics is negative.

The formula of P-value for two tailed test when the test statistics is negative.

P-value = 2 * P(Z < z test statistics) = 2 * P(Z < -2.52)

According to the z score table the probability for z score -2.52 is 0.0059, therefore

P-value = 2 * 0.0059 = 0.0118

Alpha = 0.01

Here P-value > alpha so fail to reject the null hypothesis

Do not reject H₀ since the p-value is greater than the significance level.

Conclusion: Fail to reject the null hypothesis that is there is sufficient evidence to support the claim that the average of 24 ounces of passion fruit juice is used to fill each bottle.

The accuracy of the bottling process is compromised since we do not rejecting the null hypothesis.