Consider the following hypotheses H0 79 A sample of 45 obs

Consider the following hypotheses:

H₀: ? ? 79

A sample of 45 observations yields a sample mean of 80. Assume that the sample is drawn from a normal population with a known population standard deviation of 5.1. Use Table 1.

Calculate the p-value. (Do not round intermediate calculations. Round \"z\" value to 2 decimal places and final answer to 4 decimal places.)

Calculate the p-value if the above sample mean was based on a sample of 105 observations. (Do not round intermediate calculations. Round \"z\" value to 2 decimal places and final answer to 4 decimal places.)

Solution

(a)

The test statistic is

Z=(xbar-mu)/(s/vn)

=(80-79)/(5.1/sqrt(45))

=1.32

It is a right-tailed test.

So the p-value= P(Z>1.32) = 0.0934 (from standard normal table)

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(b)Do not reject H₀ since the p-value is greater than

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(c)

The test statistic is

Z=(xbar-mu)/(s/vn)

=(80-79)/(5.1/sqrt(105))

=2.01

It is a right-tailed test.

So the p-value= P(Z>2.01) = 0.0222 (from standard normal table)

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(d)Reject H₀ since the p-value is smaller than