Question

1. You are the manager of a fast-food restaurant. The business problem is to determine whether the population mean waiting time to place an order has changed in the past month from its previous population mean value of 4.5 minute. From the past experience, you can assume that the population is normally distributed, with a population standard deviation of 1.2 minutes. You select a sample of 25 orders during a one-hour period. The sample mean is 5.1 minutes.
Determine whether there is evidence at the 0.05 level of significance that the population mean waiting time to place an order has change in the past month from its previous population mean value of 4.5 minutes.

2. A firm's advertising policy for the following year will be dependent on the market preference for their product. Thus, the company is willing to estimate with 95% CI , and standard error of 0.05.
Assume that preliminary report indicate that 25% of users prefer their product, determine the sample size to make an estimate for the preference for the preference of the firm's product.

Answer 1

1)

  

The test statistic is

  

  

At alpha = 0.05, the critical values are +/- z0.025 = +/- 1.96

Since the test statistic value is greater than the upper critical value (2.5 > 1.96), so we should reject the null hypothesis

At 0.05 significance level, there is sufficient evidence to conclude that the population mean waiting time to place an order has change in the past month from its previous population mean value of 4.5 minutes.

2) Standard error = 0.05

Or, sqrt(p(1 - p)/n) = 0.05

Or, sqrt(0.25(1 - 0.25)/n) = 0.05

Or, n = (sqrt(0.25 * 0.75)/0.05)^2

Or, n = 75