Question

Question 16 6 pts A researcher is studying the possible effect that a certain medication administered to children has on brain development. She decides to measure the effect by analyzing IQ scores of individuals who took the medication as children. She is working under the assumption that IQ scores in this population are normally distributed with a standard deviation of 15, just as in the general population. The researcher collects a sample of 40 individuals who took the medication as children. The mean IQ for the people in her sample is 94.3. Test for evidence that the mean IQ for people taking the medication as children is lower than 100, which is the mean for the general population. Use a level of significance of a = 0.01. O p = 0.0081 We do not reject the null hypothesis. There is not sufficient evidence at the 1% level of significance to suggest that individuals who took the medication as children have a mean IQ that is less than 100. O p = 0.0162 We do not reject the null hypothesis. There is not sufficient evidence at the 1% level of significance to suggest that individuals who took the medication as children have a mean IQ that is less than 100. O p = 0.0106 We reject the null hypothesis. There is sufficient evidence at the 1% level of significance to suggest that individuals who took the medication as children have a mean IQ that is less than 100. o p=0.0081 We reject the null hypothesis. There is sufficient evidence at the 1% level of significance to suggest that individuals who took the medication as children have a mean IQ that is less than 100. O p = 0.0162 We reject the null hypothesis. There is sufficient evidence at the 1% level of significance to suggest that individuals who took the medication as children have a mean IQ that is less than 100. O p = 0.0106 We do not reject the null hypothesis. There is not sufficient evidence at the 1% level of significance to suggest that individuals who took the medication as children have a mean IQ that is less than 100.

Answer 1

The statistical software output for this problem is:

One sample Z summary hypothesis test: u Mean of population H = 100 H <100 Standard deviation = 15 Hypothesis test results: Mean Sample Mean Std. Err. Z-Stat 40 94.3 2.3717082 -2403331 P-value 0.0081

Hence,

p = 0.0081 and we reject the null hypothesis.

Option 4 is correct.