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 the 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, determine whether this is sufficient evidence to reject the null hypothesis μ=30 minutes in favor of the alternative hypothesis μ≠30 minutes. Use the 0.05 level of significance.

Answer 1

As the population standard deviation is not given we need to use t-test.

Step 1 : Null and alternative hypothesis

Step 2 : Test Statistic

t = 3.354 (rounded to three decimals)

Step 3 : P value

Degrees of freedom = n-1

DF = 45 -1 = 44

Use Excel function to get p value TDIST(x,deg_freedom,tails)

=TDIST(3.354,44,2)

=0.001647

P-value = 0.002 (rounded to three decimals)

Step 4 : Decision rule

We reject the null hypothesis if p value is less than the level of significance.

P value (0.002) is less than the level of significance (0.05)

Therefore we have sufficient evidence to reject the null hypothesis.