1.A study has been conducted to determine whether the mean spending for recreational activities during the month of August differs for residents of three cities. Random samples of 30 people were selected from each city and their spending on recreation was recorded during August. The following output was generated by Excel


SUMMARY
Groups Count Sum Average Variance
City 1 30 7897.179 263.2393 3334.11
City 2 30 10322.1 344.0701 2201.818
City 3 30 6045.102 201.5034 2215.919
ANOVA
Source of variation SS Df MS F p-value
Between groups 306701.8 2 153350.9 59.3475 5.54E-17
Within groups 224803.5 87 2583.949
Total 531505.4 89


Based on the information provided, should we conclude that the three populations (cities) have equal mean spending during August? Test at the 0.05 level of significance. (Hint: Use F value in the ANOVA table above as the test statistic and find out critical F value using the appropriate F value

2.A study was recently done in which the following regression output was generated using Excel:

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.754525991
R Square 0.569309472
Adjusted R Square 0.507782253
Standard Error 1.977472261
Observations 9

ANOVA

df SS MS F Significance F
Regression 1 36.1827 36.1827 9.2529 0.0187
Residual 7 27.3727 3.9103
Total 8 63.5555

coef std err t stat p value lower95% upper 95
Intercept 4.8229 2.2045 2.1876 0.0648 -0.3900 10.0359
X 0.0538 0.0176 3.0418 0.0187 0.0119 0.0956
Given this output:
a) Write out the regression equation.
b) Interpret the regression equation
c) Interpret the value of R Square
d) Conduct a test of hypothesis if the regression model is significant