Statistics Problems: Hypothesis Testing, Correlation, and Linear Regression

Problem 1: Determining the Mean Amount of Water in 1-Gallon Bottles

1. A bottled water distributor wants to determine whether the mean amount of water contained in 1-gallon bottles purchased from a nationally known water bottling company is actually 1 gallon. You know from the water bottling company specifications that the standard deviation of the amount of water per bottle is 0.02 gallon. You select a random sample of 50 bottles, and the mean amount of water per 1-gallon bottle is 0.995 gallon.

a. Is there evidence that the mean amount is different from 1.0 gallon? (Use a. Use  = 0.01)

2.You are the manager of a restaurant for a fastfood franchise. Last month, the mean waiting time at the drive-through window for branches in your geographic region, as measured from the time a customer places an order until the time the customer receives the order, was 3.7 minutes. You select a random sample of 64 orders. The sample mean waiting time is 3.57 minutes, with a sample standard deviation of 0.8 minute.

a.At the 0.05 level of significance, is there evidence that the population mean waiting time is different from 3.7 minutes?

Correlation and Linear Regression

The table below lists the calories and sugar, in grams, in one serving of seven breakfast cereals:

a.Construct a scatter plot between Calories (  ) and Sugar ( ).

b.Compute the covariance.

c.Compute the coefficient of correlation.

d.Based on (b) and (c), what conclusions can you reach about the relationship between calories and sugar?

e.Use the least-squares method to determine the regression coefficients b0 and b1 and the linear regression equation.

f.Predict the mean sugar of a cereal with 150 calories.