Question

After the installation of a new bagel baking oven in , H&H Bagels store the general manager wanted to see if the new equipment helped increase, average bagel output rate, which earlier fell to 1,180 due to broken steam valve that Mr. Kramer sabotaged. Random sample of 16 days was taken, and the manager observed that the new oven's mean daily output rate was 1,200 with sample standard deviation of 32.

A. Based on this information, develop 95% confidence interval for the population mean (round to the nearest whole bagel) and interpret the results. Based on this interpretation would it be reasonable for the store manager to conclude that the new oven's daily output has improved? Why or why not?

B. If you were the store manager, what conclusion would you make about benefits of new oven installation in terms of increase in daily bagel production at a=0.05 significance level? Support your conclusion using five-step hypothesis testing procedure.

Answer 1

A) At 95% confidence interval the critical value is t^* = 2.131

The 95% confidence interval for population mean is

+/- t^* * s/

= 1200 +/- 2.131 * 32/

= 1200 +/- 17

= 1183, 1217

We are 95% confident that the true population mean lies in the above interval.

Since the confidence interval doesn't contain the population mean value 1180, so it would be reasonable for the store manager to conclude that the new oven's daily output has improved.

B) H₀: = 1180

   H₁: > 1180

The test statistic t = ()/(s/)

                              = (1200 - 1180)/(32/)

                              = 2.5

At alpha = 0.05, the critical value is t^* = 1.753

Since the test statistic value is greater than the critical value(2.5 > 1.753), so we should reject the null hypothesis.

So at 5% significance level, we can conclude that the new oven's daily output has improved.