Question

Please use the p value approach to conduct a hypothesis test for the following problem. Please provide detailed solutions in the four steps to hypothesis testing.

The security department of a factory wants to know whether the true average time required by night guard to walk his round is 30 minutes. If, in a random sample of 45 rounds, the night guard averaged 30.9 minutes with a`standard deviation of 1.8 minutes, determined whether this is sufficient evidence to reject the null hypothesis Mu=30 minutes in favor of the alternative hypothesis Mu is not equal to 30 minutes. Use the four steps for testing and 0.05 level of significance.

Answer 1

The security department of a factory wants to know whether the true average time required by night guard to walk his round is 30 minutes. If, in a random sample of 45 rounds, the night guard averaged 30.9 minutes with a standard deviation of 1.8 minutes.

Here we perform a four steps test:

Step 1:- Null and Alternative Hypotheses:

Null hypothesis:

Vs

Alternative hypothesis:

Step 2:- Decision Rule: We reject the null hypothesis if,

Step 3:- Computation of test statistic:

Here our appropriat test statistic is given by,

Where, number of sample observations, sample standard deviation, sample mean, hypothesized mean.

Value of test statistic:

Putting the vlue of , , and and we get

So, value of test satistic = 3.3541 and Degrees of freedom of test statistic = 45-1= 44

Now we compute p-value of the test. For t distribution p-value calculation by hand is very difficult so we compute p-value by Ms-Excel.

P-Value = P(T<3.3541) = 0.000823

[ steps for excel: in any blank cell of excel type, " =T.DIST(3.3541,44,TRUE) " -> Press Enter -> You get the P-Value ]

Step 4:- Decision:

Here we get, P-Value = 0.000823 and

So we get,

Result: We reject the null hypothesis at level .

Conclusion: The average time required by night guard to walk his round is not 30 minutes.