Question

a. State the null and alternate hypothesis, and state the claim/Draw the Bell curve and shade the appropriate tail

b. State the Critical value

c.. Compute the test value

d. State the decision

e. Conclusion

4. A machine that fills beverage cans is supposed to put 16 ounces of beverage in each can. Following are the amounts measured in a simple random sample of eight cans. Assume that the sample is approximately normal. Can you conclude that the mean volume differs from 16 ounces? Use the alpha = 0.01 level of significance. Amounts=[16.04 , 15.79 , 15.90, 15.96 , 15.84 , 15.89 , 16.08 , 15.70].

Answer 1

Answer:

a) Set the null and alternative hypotheses

The hypotheses can be stated as:

Bell curve:

b) Critical value:

The t distribution value for a two-tailed test is t_{0.005, 7} = 3.499 for degrees of freedom 7 and alpha = 0.01. So, if the computed t value is outside the 3.499 range, the null hypothesis will be rejected; otherwise, it is accepted.

c) Test statistic value:

The sample size is less than 30. So, t test is an appropriate test. The t statistic is given as

From the sample data, , Sample standard deviation (s) = 0.1262, n = 8.

By substituting all the values in t formula, we get

d) Decision:

Since, computed t value is -2.2412 which falls in acceptance region. Hence, null hypothesis cannot be rejected.

e) Conclusion:

This implies that the evidence from the sample is not sufficient to reject the null hypothesis that the population mean is 16 ounces. Then it can be conclude that, the mean volume does not differs from 16 ounces.