Problem 1
Suppose a manufacturing company makes a certain item. The time to produce each item is normally distributed around a mean of 27 minutes with a standard deviation of 2.5 minutes. Thus, the population of production times is normal in shape. Find the mean and standard deviation of the sample.
Problem 2
The average prices for a product in 12stores in a city are shown below.
$2.99, $2.85, $3.25, $3.55, $3.00, $2.99, $2.76, $3.50, $3.20, $2.85, $3.75, $3.85
Test the hypothesis that the average price is higher than $2.87. Use level of significancea = 0.05.
Problem 3
A store wishes to predict net profit as a function of sales for the next year.The following table gives the years 1998 to 2005.
Year |
Sales (thousands of dollars) |
Net Profit |
1998 |
51 |
5 |
1999 |
55 |
10.2 |
2000 |
65 |
9.6 |
2001 |
82 |
-3 |
2002 |
75 |
2.8 |
2003 |
71 |
3.2 |
2004 |
82 |
-2.3 |
2005 |
81 |
-2.6 |
(a) Graph the points from 1998 through 2005on ascatter diagram using Sales as the independent variable and Net Profit as the dependent variable.
(b) Draw the regression line on the graph you constructed in Part (a).
(c) What is the value of the coefficient of determination for this regression model? Comment on the strength of the regression line for this model.
(d) What is the predicted net profit for 2006 if sales are expected to be 125?
Solution:
Step-1: Null and Alternate Hypothesis:
Null Hypothesis: The mean price is less than or equal to $2.87.
:
A