Question

Make sure you state your hypotheses and rejection rule. Calculate your test statistic and decide whether to reject the null hypothesis or not and then explain what that conclusion means. You will need to use formulas with proper notation and draw diagrams for each of these problems.

2. From a population of coffee cans marked "12 ounces," a sample of 25 cans is selected and the contents of each can is weighed. The sample revealed a mean of 11.8 ounces with a standard deviation of 0.5 ounces. Use a .05 level of significance to test if the cans are being under filled.

Answer 1

Null Hypothesis(H0): The cans are not being under filled.

Alternative Hypothesis(H1): The cans are being under filled. (left-tailed test)

Sample size, n =25 < 30, small sample and also population standard deviation is unknown and so, we use t-test.

Test statistic, t =​​​​​​

Critical value of t at 0.05 significance level (​​​​​​) for a left-tailed test is: t-critical = -1.711

Decision criteria (or rejection rule): Since it is a left tailed test, reject the null hypothesis, H0 if t < -1.711.

Decision: Since t of -2 < -1.711, we reject the null hypothesis, H0 at 0.05 significance level.

Test statistic, t = -2 fell in the rejection region for H0 and thus, H0 is rejected.

Conclusion: There is a sufficient statistical evidence to claim that the cans are being under filled (i.e., the population mean is significantly less than 12 ounces) at 0.05 significance level.