Question

Testing: H 0 : μ = 67.9 H 1 : μ > 67.9 Your sample consists of 24 subjects with ¯ x = 83.7 giving the resulting test statistic of 1.625 . Assume that σ is unknown when conducting the hypothesis and your testing at the 0.01 significance level. Find the p-value based upon the test statistic given. P-value = Round the p-value to four decimals.

Answer 1

The null and the alternate hypothesis for the right tail test is defined as:

The population standard deviation is unknown, hence, t-distribution will be required to carry out the hypothesis testing.

The following information is provided in the problem:

• Sample size:
• The value of the test statistic : 1.625
• The significance level is

The test statistic follows the t-distribution with degrees of freedom. Here,

Therefore, follows  t-distribution with 23 degrees of freedom, that is .

The p-value is computed as the probability of the value of being greater than the value of the test statistic, . Mathematically,

The value of the right tail of the t-distribution will be calculated using the command "=T.DIST.RT()" in MS-Excel as shown below:

This implies:

Hence, the .

CONCLUSION:

Since, the p-value (0.0589) is greater than the value of the (0.01), hence, there is an insufficient evidence to reject the null hypothesis and it can, therefore, be conclude that the population mean is .