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4.26 Gifted children, Part II: Exercise 4.24 describes a study on gifted children. In this study, along with variables on the children, the researchers also collected data on the mother's and father's IQ of the 36 randomly sampled gifted children. The histogram below shows the distribution of mother's IQ. Also provided are some sample statistics.

n	36
min	101
mean	118.2
sd	6.5
max	131

(a) Perform a hypothesis test to evaluate if these data provide convincing evidence that the average IQ of mothers of gifted children is different than the average IQ for the population at large, which is 100. Use a significance level of α = 0.10.
The hypotheses for this test are:

Ho: μ = 100
Ha: μ < 100
Ho: μ > 100
Ha: μ < 100
Ho: μ = 100
Ha: μ ≠ 100
Ho: μ = 100
Ha: μ > 100

The test statistic for the hypothesis test is z = (please round to two decimal places)

The p-value for the hypothesis test is p = (please round to four decimal places)

The conclusion for this test is:

Since p ≥ α we reject the null hypothesis and accept the alternative
Since p<α we fail to reject the null hypothesis
Since p<α we reject the null hypothesis and accept the alternative
Since p ≥ α we do not have enough evidence to reject the null hypothesis
Since p ≥ α we accept the null hypothesis

(b) Calculate and interpret a 90% confidence interval for the average IQ of mothers of gifted children.
The lower bound for the confidence interval is: (please round to two decimal places)
The upper bound for the confidence interval is: (please round to two decimal places)
Interpret the confidence interval:

We are 90% confident that the sample average IQ of mothers of gifted children fall within our confidence interval
We are 90% confident that the mean IQ for mothers of gifted children falls within our confidence interval
90% of gifted mothers have IQs that fall within our confidence interval

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