* 86% 8:14 PM wamap.org b. What are the null and alternative hypotheses? .ill AT

Question

* 86% 8:14 PM wamap.org b. What are the null and alternative hypotheses? .ill AT&T; Ho: = 105; Ha: 105 Ho: = 105, Ha: > 105 0H0: = 105, Ha: #100 Ho: -100, Ha> 100 c. What is the value of the test statistic used to determine whether the mean Full Scale IQ score of the Smart County residents is higher than the national average? O.333 O-333 03.33 O-3.33 d. After analyzing the data to determine whether the mean Full Scale IQ score of the Smart County residents is higher than the national average, the P-value of.0004 was obtained O Do not reject the null hypothesis. The average Full Scale IQ of Smart County residents is not higher than the population average

Explanation / Answer

(a) WHich hypothesis test should be done?

Answer : Z test for the population mean (option A) It is because standard deviation of population is given here.

(b) Null Hypothesisi : H0 : = 100

Alternative Hypothesis : > 100

Option D is corrct.

(c) sample mean x = 105

Population stanard deviation = 15

sample size n = 100

standard error of sample mean se0 = / sqrt(N) = 15/ sqrt(100) = 15/10 = 1.5

Test statistic

Z = (x - H)/ se0 = (105 - 100)/ 1.5 = + 3.33 [Option C is correct]

critical test statistic Z = + 1.96

so Z > Zcritical

so we shall reject the null hypothesis.

P- value = 0.0004

(D) Option D is correct here . We shall rejec the null hypothesis. The average full saclae IQ of mart COunty residents is higher than the population average

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