Question

A psychologist obtains a random sample of 24 mothers in the first trimester of their pregnancy. The mothers are asked to play classical music 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 24 children in the study result in a sample mean of 105.8 and sample standard deviation of 13, is there evidence that the children have higher IQs? Use the a=0.10 level of significance. Complete parts (a) through (d). Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). Click here to view the table of critical t-values. (a) Determine the null and alternative hypotheses. H: VO (Type integers or decimals. Do not round.) (b) Identify the test statistic. (Round to two decimal places as needed.) Approximate the P-value. The P-value is in the range (c) State the conclusion for the test. O A. Reject He because the P-value is greater than the a=0.10 level of significance. OB. Do not reject Ho because the P-value is greater than the a=0.10 level of significance. O C. Reject Ho because the P-value is less than the a = 0.10 level of significance. O D . Do not reject Ho because the P-value is less than the a=0.10 level of significance. (d) State the conclusion in context of the problem. There sufficient evidence at the a= 0.10 level of significance to conclude that mothers who listen to classical music have children with higher IQs.

Answer 1

The statistic software output for this problem is:

One sample T summary hypothesis test: u: Mean of population Ho : = 100 HA: > 100 Hypothesis test results: Mean Sample Mean Std. Err. DE T-Stat P-value 105.8 2.6536139 23 2.1856985 0.0196

Null : H₀ : μ = 100

Alternative : H_A : μ > 100
Test statistics = 2.19

0.01 < p-value < 0.025

Option C)

Sufficient