Question Description
A large number of family houses underwent foreclosure in 2009. A national survey concluded that the average loss in house values during the year was $26,471 with a standard deviation of $2250. Realtors in Syracuse, New York randomly sampled 120 bids from potential buyers to determine that the average loss in home value in that area was $23,548.
- (3 points) State the null and alternative hypotheses that will help determine whether housing prices decreased by less than the national average in the Syracuse housing market.
- (3 points) Calculate the appropriate test statistic.
- (1 point) What is the p-value associated with this test statistic?
- (2 points) Using a significance level of 5%, is the null hypothesis rejected or not rejected?
- (1 point) Describe in your own words the conclusion that your hypothesis test reached about the loss of house values in Syracuse.
- ——————————————————
Two major grocery store chains in the Rochester, New York area are Wegmans Food Markets and Tops Friendly Markets. Experts predicted that Walmart would sell products at lower prices than the local chains when it opened a store in Rochester. A local newspaper collected price information on a 15-item market basket in 2002.
A researcher conducted an analysis of variance using Excel to determine if there were any significant differences in the mean prices of the market basket at the three stores. The results are presented below:
|
Item |
Tops |
Walmart |
Wegmans |
|
Bananas (1 lb.) |
0.49 |
0.48 |
0.49 |
|
Campbell's soup (10.75 oz) |
0.60 |
0.54 |
0.77 |
|
Chicken breasts (3 lbs.) |
10.47 |
8.61 |
8.07 |
|
Colgate toothpaste (6.2 oz) |
1.99 |
2.40 |
1.97 |
|
Large eggs (1 dozen) |
1.59 |
0.88 |
0.79 |
|
Heinz ketchup (36 oz) |
2.59 |
1.78 |
2.59 |
|
Jell-O (cherry, 3 oz.) |
0.67 |
0.42 |
0.65 |
|
Jif peanut butter (18 oz.) |
2.29 |
1.78 |
2.09 |
|
Milk (fat free, 1/2 gal.) |
1.34 |
1.24 |
1.34 |
|
Oscar Meyer hot dogs (1 lb.) |
3.29 |
1.50 |
3.39 |
|
Ragu pasta sauce (1 lb., 10 oz.) |
2.09 |
1.50 |
1.25 |
|
Ritz crackers (1 lb.) |
3.29 |
2.00 |
3.39 |
|
Tide detergent (liquid, 100 oz.) |
6.79 |
5.24 |
5.99 |
|
Tropicana orange juice (1/2 gal.) |
2.50 |
2.50 |
2.50 |
|
Twizzlers (strawberry, 1 lb.) |
1.19 |
1.27 |
1.69 |
|
Anova: Single Factor |
||||||
|
SUMMARY |
||||||
|
Groups |
Count |
Sum |
Average |
Variance |
||
|
Tops |
15 |
41.18 |
2.745333 |
6.974255 |
||
|
Walmart |
15 |
32.14 |
2.142667 |
4.585321 |
||
|
Wegmans |
15 |
36.97 |
2.464667 |
4.440812 |
||
|
ANOVA |
||||||
|
Source of Variation |
SS |
df |
MS |
F |
P-value |
F critical |
|
Between Groups |
2.728324 |
2 |
1.364162 |
0.255774 |
0.7755141 |
3.21994229 |
|
Within Groups |
224.0054 |
42 |
5.333463 |
|||
|
Total |
226.7338 |
44 |
a. (3 points) Describe the null and alternative hypotheses being tested in the ANOVA table.
b. (1 point) What does the “within groups sum of squares” represent (i.e. what assumption is being made to complete this calculation)?
c. (1 point) What does the “between groups sum of squares” represent (i.e. what assumption is being made to complete this calculation)?
d. (3 points) Using a level of significance of 10 percent, does Walmart charge lower prices than Wegmans and Tops? Explain.
e. (1 point) Describe the Type I error associated with this hypothesis test.
f. (1 point) How confident are you in your conclusion?
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