A mail-order business prides itself in its ability to fill customers' orders in six calendar days or less on the average.Periodically,the operations manager selects a random sample of customer orders and determines the number of days required to fill the orders.Based on this sample information,he decides if the desired standard is not being met.He will assume that the average number of days to fill customers' orders is six or less unless the data suggest strongly otherwise.On one occasion where a sample of 40 customers was selected,the average number of days was 6.65,with a sample standard deviation of 1.5 days.Can the operations manager conclude that his mail-order business is achieving its goal? Use a significance level of 0.025 to answer this question. A)Since 2.2216 2.023,reject H₀ and conclude that the mail-order business is not achieving its goal. C)Since 2.4421 2.023,reject H₀ and conclude that the mail-order business is not achieving its goal. D)Since 2.2346

Question

A mail-order business prides itself in its ability to fill customers' orders in six calendar days or less on the average.Periodically,the operations manager selects a random sample of customer orders and determines the number of days required to fill the orders.Based on this sample information,he decides if the desired standard is not being met.He will assume that the average number of days to fill customers' orders is six or less unless the data suggest strongly otherwise.On one occasion where a sample of 40 customers was selected,the average number of days was 6.65,with a sample standard deviation of 1.5 days.Can the operations manager conclude that his mail-order business is achieving its goal? Use a significance level of 0.025 to answer this question. A)Since 2.2216 < 2.4511,reject H₀ and conclude that the mail-order business is not achieving its goal B)Since 2.7406 > 2.023,reject H₀ and conclude that the mail-order business is not achieving its goal. C)Since 2.4421 > 2.023,reject H₀ and conclude that the mail-order business is not achieving its goal. D)Since 2.2346 < 2.5113,reject H₀ and conclude that the mail-order business is not achieving its goal.

Quizplus · Accepted Answer

To determine if the mail-order business is achieving its goal, we need to perform a one-sample t-test with the null hypothesis H0: μ ≤ 6 (the average number of days is six or less) and the alternative hypothesis Ha: μ > 6 (the average number of days is greater than six). 
The test statistic is t = (6.65 - 6) / (1.5 / √40) = 2.7406. 
At a significance level of 0.025 and degrees of freedom (df) = 39, the critical value for a one-tailed test is t0.025,39 = 2.023. 
Since our test statistic (2.7406) is greater than the critical value (2.023), we reject the null hypothesis and conclude that the mail-order business is not achieving its goal of filling orders in six calendar days or less on average.

A Mail-Order Business Prides Itself in Its Ability to Fill