Question

In an effort to make a healthier product, the Oriental Spice Sauce company has reduced the amount of sodium in their product to 900mg. In addition, the standard deviation of the amount of sodium should be 130. To make sure this new product continues to meet the standard, a random sample of 29 bottles is taken, and the standard deviation for the sample was 183.8264. Is there evidence at α=0.05 that the standard deviation of the sodium content exceeds the desired level? Assume the population is normally distributed.

Step 1 of 5: State the null and alternative hypotheses. Round to four decimal places when necessary.

Step 2 of 5: Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places.

Step 3 of 5: Determine the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5: Make the decision.

Reject Null Hypothesis

Fail to Reject Null Hypothesis

Step 5 of 5: What is the conclusion?

There is sufficient evidence to show that the standard deviation of the sodium content exceeds the desired level.

There is not sufficient evidence to show that the standard deviation of the sodium content exceeds the desired level.

Answer 1

(A) we have to test whether the standard deviation of the sodium content exceeds the desired level. So, it is a right tailed hypothesis test

(4 decimals)

(B) sample size is n = 29

so, degree of freedom = n-1 = 29-1 = 28

critical value = CHIINV(alpha,df)

= CHIINV(0.05,28)

= 41.337

(C) Given that sigma = 130

n = 29 and s = 183.8264

test statistic=

(D) Reject Ho because test statistic is greater than critical value

(E) There is sufficient evidence to show that the standard deviation of the sodium content exceeds the desired level.

This is because the result is significant as we have rejected the null hypothesis. This means that the standard deviation is significantly greater than 130