Question

When operating normally, a manufacturing process produces tablets for which the mean weight of the active ingredient is 5 grams, and the standard deviation is 0.025 gram. For a random sample of 12 tables the following weights of active ingredient (in grams) were found:

5.01 4.69 5.03 4.98 4.98 4.95 5.00 5.00 5.03 5.01 5.04 4.95

Without assuming that the population variance is known, test the null hypothesis that the population mean weight of active ingredient per tablet is 5 grams. Use a two-sided alternative and a 5% significance level. State any assumptions that you make.

State the following:

1. The null and alternate hypothesis statements

2. The significance level

3. The test statistic

4. Decision Rules

5. Calculate Test Statistic and find the p-value

6. Interpret the results of the test.

7. Assumptions

Answer 1

= 4.9725

s = 0.0936

1) H₀: = 5

    H₁: 5

2) The signiicance level is 0.05.

3) The test statistic t = ()/(s/)

                                 = (4.9725 - 5)/(0.0936/)

                                 = -1.02

At 5% significance level, the critical value is t_{0.025, 11} = +/- 2.201

Reject H₀, if t < -2.201 or t > 2.201

Since the test statistic value is not less than the lower critical value (-1.02 > -2.201), so we should not reject H₀.

P-value = 2 * P(T < -1.02)

             = 2 * 0.1648

             = 0.3296

At 5% significance level there is sufficient evidence to conclude that the population mean weight of active ingredient per tablet is 5 grams.

Assume that is unknown.