Question

A random sample of 15 students showed that their average fear of math was 84.8 on a 1-100 scale, with a standard deviation of 2.7. At the α = .01 significance level, test the claim that the average fear of math of all students is below 85 on this scale. b) Suppose now the same mean and standard deviation were found in a random sample of 10000 students. Again, at the α = .01 significance level, test the claim that the average fear of math of all students is below 85.

Answer #1

a) As we are testing here whether the mean is below 85, therefore the test statistic here is computed as:

For n - 1 = 14 degrees of freedom, as this is a one tailed test,
the p-value is obtained from the t distribution tables as:

p = P( t_{14} < -0.2869) = 0.3892

As the p-value here is 0.3892 > 0.01, therefore the test is not significant and we dont have sufficient evidence here that population mean is below 85 here.

b) For n = 10,000 the test statistic here is computed as:

For 10000 - 1 = 9999 degrees of freedom, the p-value here is
obtained from the t distribution tables as 0 because the test
statistic magnitude is very high. **Therefore the test is
significant here and we can reject the null hypothesis and conclude
that we have sufficient evidence that the population mean is less
than 85 here.**

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