Score: 0 of 1 pt 7 of 8 (2 complete) HW Score: 5.63%, 0.45 of 8 pts Instructor-c

Question

Score: 0 of 1 pt 7 of 8 (2 complete) HW Score: 5.63%, 0.45 of 8 pts Instructor-created question Question Help A psychologist obtains a random sample of 20 mothers in the first trimester of their pregnancy. The mothers are asked to play Mozart in the house at least 30 minutes each day untill they give birth. After 5 years, the child is administered an IQ test. It is known that IQs are normally distributed with a mean of 100. If the lQs of the 20 children in the study result in a sample mean of 104.2 and sample standard deviation of 14, is there evidence that the children have higher IQs? Use the 0.05 level of significance. Complete parts (a) through (d) (a) Determine the null and alternative hypotheses. A.HO: s 100 H1:100 0 B. Ho : 100 H1 : 100 C. Ho: 104.2 H1 : > 104.2 OF. Ho: p 100 H: p 100 (b) Calculate the test statistic and the P-value. t-statistics (Round to four decimal places as needed.) P-value # | | (Round to three decanal places as needed.) (c) State the conclusion for the test Choose the correct answer below. A. Reject Ho because the P-value is greater than the # 0.05 level of significance. B. Do not reject Ho because the P-value is greater than the 0.05 level of significance. Reject Ho because the P-value is less than the -o05 level of significance. Do not reject Ho because the P-value is less than the 41-o05 level of significance C. D. (d) State the conclusion in context of the problem There | | sufficient evidence at the = 0 05 level of significance to conclude that mothers who listen to Mozart have children 0 A, with higher than 100 average IQ O B. with an average IQ of 100 ° C. with an average IQ different from 100, D. with an average IQ of less than 100

Explanation / Answer

Ans:

a)Option A is correct.

right tailed test.

b)Test statistic:

t=(104.2-100)/(14/sqrt(20))

t=1.3416

df=20-1=19

p-value=tdist(1.3416,19,1)=0.098

c)As,p-value=0.098>0.05,we Do not reject H0.

Option B is correct.

d)There is not sufficient evidence to conclude that mothers who listen to Mozart have children with higher than 100 average IQ.

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