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 until 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 IQs of the 20 children in the study result in a sample mean of 104.1 and sample standard deviation of 15, is there evidence that the children have higher IQs? Use the a=0.05 level of significance. Complete parts (a) through (d).b) Calulate the P-value.P-value+_______(round to three decimal places as needed.c) State the conclusion for the test.Choose the correct Anser below.a. Do not reject H0 becasue the P-value is less than the a-0.05 level of significanceb. Reject H0 because the p-value is greater than the a=0.05 level of significancec. Do not reject H0 because the P-value is less than the a-0.05 level of signifcance.d. Reject H0 because the p-value is less than the a=0.05 level of significance.d) State the conclusion in context of the problem.There (1)_sufficient evidence at the a=0.05 level of significance to conclude that mothers who listen to Mozart have children with hogher IQs.(1)is not_is

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26-11-2019
Mathematics

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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 until 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 IQs of the 20 children in the study result in a sample mean of 104.1 and sample standard deviation of 15, is there evidence that the children have higher IQs? Use the a=0.05 level of significance. Complete parts (a) through (d).b) Calulate the P-value.P-value+_______(round to three decimal places as needed.c) State the conclusion for the test.Choose the correct Anser below.a. Do not reject H0 becasue the P-value is less than the a-0.05 level of significanceb. Reject H0 because the p-value is greater than the a=0.05 level of significancec. Do not reject H0 because the P-value is less than the a-0.05 level of signifcance.d. Reject H0 because the p-value is less than the a=0.05 level of significance.d) State the conclusion in context of the problem.There (1)_sufficient evidence at the a=0.05 level of significance to conclude that mothers who listen to Mozart have children with hogher IQs.(1)is not_is

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AlonsoDehner AlonsoDehner · Answer 1 · 2019-11-26T11:08:02+01:00

Answer:

Is not

Step-by-step explanation:

Given that population mean of IQ after 5 years for a child is 100.

A sample of 20 mothers in the first trimester of their pregnancy are asked to play Mozart in the house at least 30 minutes each day until they

give birth. This sample had a mean of 104.1 with std dev =15

Since population std dev is not known and sample size is small, we can use t test

[tex]H_0: \bar x =100\\H_a: \bar x >100[/tex]

(Right tailed test at 5% significance level)

Std error of sample mean = [tex]\frac{15}{\sqrt{20} } =3.35\\[/tex]

Test statistic t = mean difference / std error

= 1.222

p value = 0.1187=0.119

Do not reject H0 becasue the P-value is not less than the a-0.05 level of significance

There (1)_____is not________sufficient evidence at the a=0.05 level of significance to conclude that mothers who listen to Mozart have children with higher IQs.