Infants weighing less than 1,500 grams at birth are classed as "very low birth weight." Low...
Infants weighing less than 1,500 grams at birth are classed as "very low birth weight." Low birth weight carries many risks. IQ tests are designed to produce IQ scores varying Normally with standard deviation ?=15 . They are also scaled so that the mean score in a large population should be ?=100 . One study followed 113 male infants with very low birth weight to adulthood. At age 20 , the mean IQ score for these men was ?¯=87.6 . We suspect that the very‑low‑birth‑weight population has a mean IQ score less than 100 . A hypothesis test would have the null hypothesis that the mean IQ of very‑low‑birth‑weight male babies is 100 against the alternative hypothesis that the mean is less than 100 . Select the correct statement concerning what it means to make a Type I error and a Type II error in this setting.
a) A Type I error would be concluding that the mean IQ of very‑low‑birth‑weight male babies is less than 100 when in reality the mean is 100 . A Type II error would be failing to reject that the mean IQ of very‑low‑birth‑weight male babies is 100 when in reality the mean is less than 100 .
b) A Type I error would be concluding that the mean IQ of very‑low‑birth‑weight male babies is greater than 100 when in reality the mean is less than 100 . A Type II error would be failing to reject that the mean IQ of very‑low‑birth‑weight male babies is 100 when in reality the mean is less than 100
c) A Type I error would be failing to reject that the mean IQ of very‑low‑birth‑weight male babies is less than 100
when in reality the mean is less than 100 . A Type II error would be concluding that the mean IQ of very‑low‑birth‑weight male babies is less than 100 when in reality the mean is greater than 100
d) A Type I error would be failing to reject that the mean IQ of very‑low‑birth‑weight male babies is 100
when in reality the mean is less than 100 . A Type II error would be concluding that the mean IQ of very‑low‑birth‑weight male babies is less than 100 when in reality the mean is 100 .
Homework Answers
Since, sample mean is an unbiased estimator of poulation mean(Given sample size is large)
we can conclude that the mean IQ score at age 20 for all very-low-birth-weight males is equal to 87.6
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