Question

A small college with 300 students claims that its students have an average IQ of 100. A sample of 9 of the 30 students in the intermediate statistics class had an average of 110 with a calculated standard deviation of 12. IQ tests, like most standardized tests, are designed so that the distribution of scores is approximately normal. Using a level of significance of 0.01, is there any evidence that the students in this class are any dumber or smarter than the rest of the college population? State relevant hypotheses and conclusions.

Answer 1

Null Hypothesis (Claim)

Alternative Hypothesis (Two tailed test )

Under H0, the test statistic is

Significance Level

Degrees of freedom = n-1= 9-1 = 8

The critical value of t for 8 df at 1% significance level is +/-3.355

The P-Value is .0369

Since p value is greatre than significance level, Fail to Reject H0.

Hence at 1% significance level, twe have enough evidence to support the claim that students have an average IQ of 100.

Hence the the students in this class are smarter than the rest of the college population.