Question

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 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 104.4 and sample standard deviation of 14​, is there evidence that the children have higher​ IQs? Use the alpha equals 0.05 level of significance. Complete parts ​(a) through ​(d). ​(a) Determine the null and alternative hypotheses. Upper H 0​: ▼ mu p sigma ▼ less than not equals greater than equals 100 Upper H 1 : ▼ mu sigma p ▼ less than greater than not equals equals 100 ​(b) Calculate the​ P-value. ​P-valueequals nothing ​(Round to three decimal places as​ needed.) ​(c) State the conclusion for the test. Choose the correct answer below. A. Do not reject Upper H 0 because the​ P-value is less than the alpha equals 0.05 level of significance. B. Do not reject Upper H 0 because the​ P-value is greater than the alpha equals 0.05 level of significance. C. Reject Upper H 0 because the​ P-value is greater than the alpha equals 0.05 level of significance. D. Reject Upper H 0 because the​ P-value is less than the alpha equals 0.05 level of significance. ​(d) State the conclusion in context of the problem. There ▼ is not is sufficient evidence at the alpha equals 0.05 level of significance to conclude that mothers who listen to Mozart have children with higher IQs. Click to select your answer(s).

Answer 1

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