Question

2) Bon Air Elementary School has 300 students. The principal of the school thinks that the average IQ of students at Bon Air is 110. To prove her point, she administers an IQ test to 20 randomly selected students. Among the sampled students, the average IQ is 107 with a standard deviation of 6, suggesting that the average IQ is lower than she thought. Based on these results, should the principal accept or reject her original hypothesis? Assume a significance level of 0.01.

a) Write the appropriate hypotheses. Be sure to define any variables you introduce.

b) Find the P-value. Use your calculator.

c) State your conclusions.

Answer 1

given data are:-

sample mean () = 107

sample sd (s) = 6

sample size (n ) =20

a).hypothesis:-

[ where, is the true(population) average IQ of students at Bon Air ]

the principal's claim is the null hypothesis.

b).test statistic :-

df = (n-1) = (20-1) = 19

p value :-

[ use calculator or in excel type =T.DIST(-2.236,19,TRUE)]

c).decision:-

p value = 0.0188 > 0.01 (alpha)

so, we fail to reject the null hypothesis.

conclusion:-

Based on these results, the principal should accept her original hypothesis.

there is some evidence to support the claim of the principal at 0.01 level of significance.

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