In: Statistics and Probability
1. A country club wants to inspect the effects of a new marketing campaign that attempts to get more people within the community to become members. In many communities, when people buy a house in the area, they receive a “Welcome Wagon” gift basket containing coupons to local restaurants. The idea of the marketing campaign is to include a free two month membership to the country club in the gift basket with the hope that once “new” residents try the country club then at least a certain proportion will want to become real members. One member of the Club’s Executive Council believes that at least 80% of the people who receive the coupons for the free membership will use the coupon. In a sample of 205 new residents who received the coupon for the two month free membership, there were 136 people who actually took advantage of the free two month membership. When testing the hypothesis that at least 80% of the people that receive the coupon actually use it, what is the test statistic? (please round your answer to 2 decimal places)
2. The following results are from data concerning the amount
withdrawn from an ATM machine based on the amount of time spent at
the ATM machine (SECONDS) and the gender, FEMALE (dummy variable =
1 for females and = 0 for males) and an interaction term,
SECONDS*FEMALE
SUMMARY OUTPUT |
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Regression Statistics |
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Multiple R |
0.503 |
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R Square |
||||||
Adjusted R Square |
||||||
Standard Error |
||||||
Observations |
50 |
|||||
ANOVA |
||||||
df |
SS |
MS |
F |
Significance F |
||
Regression |
2728.7 |
5.19 |
0.004 |
|||
Residual |
24161.8 |
525.3 |
||||
Total |
32348 |
Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
|
Intercept |
131.9 |
23.51 |
5.89 |
0 |
91.03 |
185.67 |
Seconds |
-1.93 |
0.668 |
0.002 |
-3.401 |
-0.839 |
|
Female |
-73.8 |
30.6 |
-2.26 |
-137.33 |
-8.07 |
|
Seconds*Female |
2.4 |
0.81 |
2.8 |
0.007 |
0.67 |
Based on the regression results, what is the predicted amount
withdrawn for a male who spends 32 at the ATM machine? (please
express your answer using 1 decimal places)
(1).
As per the given information,
-The sample size (n) is 205.
-The number of people who actually took advantage of the free two month membership (x) is 136.
- The club member believes that at least 80% of the people who receive the coupons for the free membership will use the coupon.
-The hypothetical value of the population proportion (p) is 0.80.
The estimated proportion is,
The test statistic is,
Therefore, the value of the test statistic is -4.89.
(2).
Let y be the amount withdrawn from an ATM machine.
The regression equation is,
The predicted amount withdrawn for a male who spends 32 at the ATM machine is,
Therefore, predicted amount withdrawn for a male who spends 32 at the ATM machine is 73.1.