Consider the following hypotheses: H 0 : 186 A sample of 75 observations results

Question

Consider the following hypotheses:

H0: 186

A sample of 75 observations results in a sample mean of 176. The population standard deviation is known to be 24. Use Table 1.

What is the critical value for the test with = 0.10 and with = 0.01? (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)

Does the above sample evidence enable us to reject the null hypothesis at = 0.10?

Does the above sample evidence enable us to reject the null hypothesis at = 0.01?

Consider the following hypotheses:

Explanation / Answer

Here population standard deviation is known so we do z-test.

Part a)

We use normal table to get the critical values:

a = 0.10: Critical value = -1.28

a = 0.01: Critical value = -2.33

Part b)

Part 1:

Z = ( x bar - µ) / ( s/Ön)

= (176-186)/(24/Ö75)

= -3.61

Test Statistic = -3.61

The test statistics is less than the critical value (-3.61 <-1.28); we reject the null hypothesis.

Part 2:

Yes since the value of the test statistic is less than the negative critical value

Part c)

The test statistics is less than the critical value (-3.61 <-2.33); we reject the null hypothesis.

Yes since the value of the test statistics is less than the negative critical value.

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