Question

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 443443 gram setting. It is believed that the machine is underfilling the bags. A 1515 bag sample had a mean of 434434 grams with a standard deviation of 1717. A level of significance of 0.10.1 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Reject H0 if t < _________

Answer 1

Given that a manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 443grams setting. It is believed that the machine is underfilling the bags. A, n = 15 bag sample had a mean of = 434 grams with a standard deviation of s= 17. A level of significance of 0.10 is used. Assuming the population distribution is approximately normal.

Based on the claim the hypotheses are:

Thus based on the hypothesis, it will be a left tailed test, since the population standard deviation is unknown hence t-distribution is applicable for hypothesis testing.

Rejection region:

Based on the type of hypothesis and given level of significance the critical value for the rejection region is calculated by excel formula for t-distribution which takes significance level and degree of freedom as the parameter. The degree of freedom is calculated as df = n-1= 15- 1=14.

The excel formula used is =T.INV(0.10, 16), thus the tc computed as -1.345

Reject Ho if t < -1.345

Test statistic:

Conclusion:

Since the t <tc hence we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the machine is underfilling the bags.

Note: I believe that the data values were typed twice simulataneously, please check the data first.