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A sample of 9 respondents was randomly selected to analyze their weekly grocery expenses. Individual expenses were assumed to be independent and normally distributed with an unknown average and standard deviation of $15. The sample mean was $171.60 and the sample standard deviation was $16.50. The document asks to test if the population mean differs from $180, if it is below $180, and to estimate the population average with 99% confidence.

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A sample of n = 9 respondents was selected at random to analyze their weekly grocery expenses.
Individual records are assumed to be independent normally distributed with unknown average ()
and population standard deviation = $15.00 Sample summaries were found as follows: Sample
Mean = X = $171.60 and Sample SD = s = $16.50
1. At significance level = 0.05, do you have sufficient evidence that the population mean differs
from 0 = $180? State the rejection rule and show the test statistic value.
2. At significance level = 0.05, is there sufficient evidence that the population mean is below 0 =
$180? State the rejection rule and show the test statistic value.
3. Estimate the population average with confidence C = 0.99. Show margin of error and critical
value needed

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