Question

A Rollercoaster’s auditors estimate that the average daily loss from those illegally riding without tickets is at least $200, but wants to determine the accuracy of this statistic. The company researcher takes a random sample of losses over 64 days and finds that X = $198 and s = $15. Test at α = 0.01.

Answer 1

Given that a Rollercoaster’s auditors estimate that the average daily loss from those illegally riding without tickets is at least = $200. So, to test the assumption The company researcher takes a random sample of losses over 64 days and finds that X = $198 and s = $15.

hence the Hypotheses are:

Based on the hypothesis it will be a left-tailed test.

Since the Sample size is greater than 30 but the population standard deviation is not known hence t-distribution is used to test the hypothesis.

Rejection region:

Based on the significance level 0.01 and degree of freedom = n-1= 64-1= 64 the critical value for rejection region is calculated using excel formula for t distribution which is =T.INV(0.01,63) thus results in tc = -2.387

So, reject the Ho if t <-2.387

Test Statistic:

The test statistic is calculated as:

P-value:

The P-value is computed using excel formula for t distribution using the t-statistic calculated above and the degree of freedom as =T.DIST(-1.067,63,TRUE), thus P-value computed as 0.1451.

Conclusion:

Since the P-value is greater than 0.01 and t > tc hence we fail to reject the null hypothesis and conclude that there is insufficient evidence to warrant the accuracy that the average daily loss from those illegally riding without tickets is at least = $200.

Feel free to ask if any problem remains.