Riley, a child psychologist, claims that for all samples of size 40 from the population of infant boys and all samples of size 40 of newborn girls, the mean of the sampling distribution of the difference in sample means (boys minus girls) is 0.2 month. Is Riley correct? (A) Yes, the mean is 8.1−7.9=0.2 month. (B) No, the mean is 0.8−0.7=0.1 month. (C) No, the mean is 8−8=0 months. (D) No, the mean is 8.1−0.8=7.3 months. (E) No, the mean is 7.9−0.7=7.2 months
Child psychologists study the time, in months, that it takes for infant boys and girls to say their first words. For a certain population, the distributions of time for both populations have the same mean and have the same standard deviation, μ=8 months and σ=1.4 months. Two independent random samples of infant boys and girls were taken, and the time it took for the infants in each sample to say their first words was recorded. The summary statistics for the number of months are shown in the following table.
| n | Sample mean | s | |
| Boys | 40 | 8.1 | 0.8 |
| Girls | 40 | 7.9 | 0.7 |
Riley, a child psychologist, claims that for all samples of size 40 from the population of infant boys and all samples of size 40 of newborn girls, the mean of the sampling distribution of the difference in sample means (boys minus girls) is 0.2 month. Is Riley correct?
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(A) Yes, the mean is 8.1−7.9=0.2 month.
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(B) No, the mean is 0.8−0.7=0.1 month.
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(C) No, the mean is 8−8=0 months.
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(D) No, the mean is 8.1−0.8=7.3 months.
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(E) No, the mean is 7.9−0.7=7.2 months.I am choosing between A and C. The sample mean of the sampling distribution should equal the population mean. Therefore, the mean should be 8-8 which would be zero. But she is discussing the
sample of size 40. Which I suppose would still mean that the sample mean is 8 for each of them, but I don't know. I am confused.
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