You wish to test the following claim (HaHa) at a significance level of =0.10. Ho

Question

You wish to test the following claim (HaHa) at a significance level of =0.10.

      Ho:=86.5
      Ha:86.5
You believe the population is normally distributed and you know the standard deviation is =8.3. You obtain a sample mean of M=83.2 for a sample of size n=16.

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value = ±

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

The test statistic is...

in the critical region

not in the critical region

This test statistic leads to a decision to...

reject the null

accept the null

fail to reject the null

As such, the final conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 86.5.

There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 86.5.

The sample data support the claim that the population mean is not equal to 86.5.

There is not sufficient sample evidence to support the claim that the population mean is not equal to 86.5.

You wish to test the following claim (H.) at a significance level of = 0.10. 14: -86.5 Ha : 86.5 You believe the population is normally distributed and you know the standard deviation is What is the critical value for this test? (Report answer accurate to three decimal places.) 8.3. You obtain a sample mean of M 83.2 for a sample of size n-16 critical value = What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic - The test statistic is... in the critical region not in the critical region This test statistic leads to a decision to reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 86.5 There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 86.5. The sample data support the claim that the population mean is not equal to 86.5 There is not sufficient sample evidence to support the claim that the population mean is not equal to 86.5.

Explanation / Answer

The statistical software output for this problem is:

One sample Z summary hypothesis test:
: Mean of population
H0 : = 86.5
HA : 86.5
Standard deviation = 8.3

Hypothesis test results:

Hence,

Critical value = + 1.645

Test statistic = -1.590

Not in the critical region

Fail to reject the null

There is not sufficient evidence to support the claim that the population mean is not equal to 86.5. Option D is correct.

Mean n Sample Mean Std. Err. Z-Stat P-value 16 83.2 2.075 -1.5903614 0.1118

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