The American Research Group, Inc. conducted a telephone survey of a random sampl
ID: 3221095 • Letter: T
Question
The American Research Group, Inc. conducted a telephone survey of a random sample of 1,100 U.S. adults in a recent year and determined that the average amount of planned spending on gifts for the holiday season was $854 and that 40% of the purchases would be made from catalogs. Shown below are the average amounts of planned spending on gifts for the holiday season for 11 years along with the associated percentages to be made from catalogs.
Year Average Spending ($) Percentage Purchases to Be Made from Catalogs
1 1,037 44
2 976 42
3 1,004 47
4 942 47
5 907 50
6 859 51
7 431 43
8 417 36
9 658 26
10 646 42
11 854 40
Develop a regression model to predict the number of rentals per day by the average family income. Comment on the output.
For alpha = .01 the value of the test statistic is t =
__________ , so the decision is to fail to reject / to reject the null hypothesis
Explanation / Answer
Descriptive Statistics
Mean Std. Deviation N
Y 42.5455 7.01945 11
X 7.9373E2 222.05139 11
Coefficients(a)
Unstandardized Coefficients Standardized Coefficients
Model B Std. Error Beta t Sig.
1 (Constant) 30.115 7.519 4.005 0.003
X 0.016 .009 0.495 1.711 0.121
a. Dependent Variable: Y
here X = the average amounts of planned spending on gifts for the holiday season
Y = the associated percentages to be made from catalogs
the regression model of the data is Y = 30.115 + 0.016X
the number of rentals per day by the average family income is Y = 30.115+854(0.016) = 884.131~884
null hypothesis H0:B1 = 0
alternative hypothesis H1:B1 not = 0
test statistics t = b1/SE(b1) ~ tn-2 = 0.016/0.009 = 1.71
from t-tables the critical value of 't' at 1% level with n-2 = 11-2 = 9 df is 2.821
therefore calculated value < table value (1.71<2.821)
therefore H0 is accepted i.e we may conclude that the regression coefficient is not significant
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