1. X is normally distributed with a mean of 10 and a standard deviation of 3. Suppose that you randomly select a sample with sample size =4. Calculate the following probabilities of X ¯.
P(X ¯>15)=
P(X ¯<7.3)=
2. The regular gas price of gas stations in town A is normally distributed with a mean of 3.75 and a standard deviation of 0.3.
Suppose that I randomly choose five gas stations in town A. What is the probability that the sample mean of the regular gas price is higher than 3.68?
Suppose that I randomly choose three gas stations in town A. What is the probability that the sample mean of the regular gas price is lower than 3.79?
3. According to the claim of the manager of a pizza restaurant, pizza delivery time is normally distributed with a mean of 45 minutes and a standard deviation of 6 minutes. Now you suspect that the mean delivery time may be longer than 45 minutes. (Adapted from Bowerman (2012): 287)
Suppose that you draw a random sample of 4 pizza delivery times and that your random sample produces a sample mean of 48. Would you trust the manager's claim? Why or why not? Calculate p-value and explain.
Suppose that you drawa random sample of 36 pizza delivery times and that your random sample produces a sample mean of 48. Would you trust the manager's claim? Why or why not? Calculate p-value and explain.
4. According to the manager of a supermarket in this town, the number of customers per day is normally distributed with a mean of 400 and a standard deviation of 40. Now you suspect that the mean number of customers may be lower than 400.
Suppose that you draw a random sample of six days and that your random sample produces a sample mean of 395. Would you trust the manager's claim? Why or why not? Calculate p-value and explain.
Suppose that you draw a random sample of six days and that your random sample produces a sample mean of 360. Would you trust the manager's claim? Why or why not? Calculate p-value and explain.
5. Refer to the following data (Data: VideoGames2)
Calculate 95% confidence interval of the mean rating and explain it in English.
Can we be 95% confident that the population mean rating is higher than 40?
6. The following data shows the relationship between the outdoor temperature (X) and natural gas consumption (Y) of a certain city (Data: FuelCon1).
Write out the regression model.
Draw the X-Y scatter plot and add the regression line.
Interpret or explain the values of the followings:
Coefficient of X:
P-value of X coefficient:
R square:
F significance:
Use the regression model and predict fuel consumption when X = 41.
7. The following data shows the relationship between the advertising expense (X) and sales volume (Y) (Data: Advertising).
Write out the regression model.
Draw the X-Y scatter plot and add the regression line.
Interpret or explain the values of the followings:
Coefficient of X:
P-value of X coefficient:
R square:
F significance:
Use the regression model and predict sales volume when X = 11.