a random sample of 10 observations is selected from a normal population. The sam

Question

a random sample of 10 observations is selected from a normal population. The sample mean was 15 and the sample standard deviation 5.0. Using the 0.010 significance level:
a random sample of 10 observations is selected from a normal population. The sample mean was 15 and the sample standard deviation 5.0. Using the 0.010 significance level:
a random sample of 10 observations is selected from a normal population. The sample mean was 15 and the sample standard deviation 5.0. Using the 0.010 significance level:

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: < 10
Alternative hypothesis: > 10

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample z-test.

Analyze sample data. Using sample data, we compute the standard error (SE), z statistic test statistic (z).

SE = s / sqrt(n)

S.E = 1.5811

z = (x - ) / SE

z = 3.16

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a z statistic test statistic of 3.16.

Thus the P-value in this analysis is 0.0008

Interpret results. Since the P-value (0.008) is less than the significance level (0.01), we have to reject the null hypothesis.

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