SOLUTION: A department store management claims that families spend an average of $630 on gifts during the Christmas season. A sample of 105 families showed that they spent an average of $66

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Question 246044: A department store management claims that families spend an average of $630 on gifts during the Christmas season. A sample of 105 families showed that they spent an average of $660 on gifts during the past Christmas season with a standard deviation of $165. Test that the 5% significance level if the mean amount spent on gifts during the holiday by all families is different from $630.(could you please show all 8 steps).
Answer by stanbon(75887) About Me  (Show Source):
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A department store management claims that families spend an average of $630 on gifts during the Christmas season.
A sample of 105 families showed that they spent an average of $660 on gifts during the past Christmas season with a standard deviation of $165.
Test at the 5% significance level if the mean amount spent on gifts during the holiday by all families is different from $630.
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Ho: u = 630
H1: u is not equal to 630
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CV: 2-tail test at 5% with df = 104: t = +/-1.983
TS: t(660) = (660-630)/[165/sqrt(105)] = 1.8631
p-value = 2*P(t>1.8631 with df=104) = 2(0.0326) = 0.0653
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Conclusion: Since the p-value is greater than 5%, fail to
reject Ho. The mean amount spent is different from $630.
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Cheers,
Stan H.