Question

Question 5: Hypothesis Testing: Each question is worth 7.5 marks: Total A. Suppose we know the standard deviation of the population is 3.7. We have a sample size of 625. We also have a sample mean of 46. We also have a population mean of 43. We want to test the hypothesis for the sample mean with 78% confidence level and do a two-tailed test on the hypothesis. State the null and alternate hypothesis for the sample mean and then test the hypothesis to see if you will accept or reject the hypothesis. Please provide all calculations. B. Suppose we know the sample standard deviation is 10. We have a sample size of 25. We also have a sample mean of 116. We also have a population mean of 118. We want to test the hypothesis for the sample mean with 98% confidence level and do a two-tailed test on the hypothesis. State the null and alternate hypothesis for the sample mean and then test the hypothesis to see if you will accept or reject the hypothesis. Please provide all calculations.

Answer 1

A)

Null and Alternative hypothesis:

This corresponds to a two-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

Test statistic:

Critical value:

At = 1-0.78 = 0.22, critical value of a two tailed test, from standrad normal table = 1.23

Conclusion:

As z = 20.27 > = 1.23, we reject the null hypothesis.

There is enough evidence to claim that population mean is different than 43, at 0.22 significance level.

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B)

Null and Alternative hypothesis:

This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.

Test statistic:

df = n-1 = 25-1= 24

Critical value:

At = 1-0.98 = 0.02 and df = 14, critical value of a two tailed test, from students t-table = 2.492

Conclusion:

As |t| = 1 <   = 2.492, we fail to reject the null hypothesis.

There is not enough evidence to claim that population mean is different than 118, at 0.02 significance level.