Question

4. A company that manufactures chocolate bars is particularly concerned that the mean weight of a chocolate bar is not greater than 6.03 ounces. The company hires an independent consultant, and she randomly selects 50 chocolate bars, where the sample mean is 6.0340 ounces and the sample standard deviation is .02 ounces. Using an alpha level of .01 (also called a level of significance), conduct a single sample hypothesis test to test that the population mean weight of a chocolate bars is greater than 6.03 ounces. When you’ve completed this initial test, conduct a sensitivity analysis by testing again using an alpha level of .10. and choose the correct answer below. * Use the t table to get your critical t value.

a. Reject the null at alpha = .01 ; Reject the null at alpha = .10

b. Fail to reject the null at alpha = .01 ; Reject the null at alpha = .10

c. Fail to reject the null at alpha = .01 ; Fail to reject the null at alpha = .10

d. Insufficient evidence that population mean weight is more than 6.03 ounces at alpha = .01 ; Sufficient evidence that population mean weight is more than 6.03 ounces at alpha = .10

e. Both b and d are correct

Answer 1

using t value, if the calculated t value is greater than the critical value then we reject the null hypothesis and when the t calculated is less than t critical, then we failed to reject the null hypothesis.

we have degree of freedom = 9

using student's t distribution table, we get

t critical = 2.82 for 0.01 significance level.

calculated t value is 2.11, means less than 1.83, So we failed to reject the null hypothesis

Thus, we failed to reject the null hypothesis and we can conclude that we have insufficient evidence, the government should purchase the fleet.

Option B is correct.

but if we look at the p value concept

Using degree of freedom 9 and t calculated value = 2.11, using the student's t distribution table, we get

p value = 0.0320, this p value is more than 0.01 and less than 0.10

So, the result is significant at 0.10 level of significance and result is insignificant at 0.01 level of significance because p value is less than 0.10 and more than 0.01.

So, this makes option D correct choice

Overall, Option B and D are correct, means the correct answer option E