A local church parish wants to raise money to add to their campus. In a sample from a previous fund raising campaign, the parish found that of the 134 people in the sample they contacted, that 67 actually contributed money. Of those that contributed money, the average contribution was $893 with a standard deviation of $282. In the recent fundraising campaign, a sample of 94 people revealed that 49 have contributed money with an average contribution of $1,180 and a standard deviation of $371. When testing (at the 5% level of significance) whether the proportion of peole who are contributing has increased, what is the test statistic? (please round your answer to 2 decimal places)

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A local church parish wants to raise money to add to their campus. In a sample from a previous fund raising campaign, the parish found that of the 134 people in the sample they contacted, that 67 actually contributed money. Of those that contributed money, the average contribution was $893 with a standard deviation of $282. In the recent fundraising campaign, a sample of 94 people revealed that 49 have contributed money with an average contribution of $1,180 and a standard deviation of $371. When testing (at the 5% level of significance) whether the proportion of peole who are contributing has increased, what is the test statistic? (please round your answer to 2 decimal places)

Expert Solution
Step 1

Given,

Sample from a previous fund raising campaign has

n1=134X1=67x1=$893s1=$282

Sample proportion is

p1=X1n1    =67134    =0.5

Sample from a recent fund raising campaign has

n2=94X2=49x2=$1,180s2=$371

Sample proportion is

p2=X2n2    =4994    =0.52

Level of significance is α=5%=0.05.

Step 2

Hypotheses:

H0: The proportion of people who are contributing has not increased from the previous fund raising campaign. i.e. P1P2

H1: The proportion of people who are contributing has increased from the previous fund raising campaign. i.e. P1<P2

The test is a left tailed test.

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