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According to the National Health and Nutrition Survey (NHANES) sponsored by the U.S. government, a random...

According to the National Health and Nutrition Survey (NHANES) sponsored by the U.S. government, a random sample of 712 males between 20 and 29 years of age and a random sample of 1,001 males over the age of 75 were chosen and the weight of each of the males were recorded (in kg). Do the data provide evidence that the younger male population weighs more (on average) than the older male population? Use “Y” for ages 20-29 and “S” for ages 75+. If was found that x̅Y = 83.4, sY = 18.7, x̅S = 78.5, sS = 19.0.

Suppose the calculated confidence interval was (3.546, 6.254). What is the correct interpretation of this confidence interval?

  1. We are 95% confident that the true mean difference between the weight of males 20-29 and the weight of males 75+ lies between 3.546 and 6.254 kg.
  2. We are 95% confident that the true difference between the mean weight of males 20-29 and the mean weight of males 75+ lies between 3.546 and 6.254 kg.
  3. 95% of the time, the difference in the mean weight of males 20-29 and the mean weight of all males 75+ will lie between 3.546 and 6.254 kg.
  4. We are 95% confident that the true difference between the sample mean weight of males 20-29 and the same mean weight of males 75+ lies between 3.546 and 6.254.

A university administrator sampled the academic records of both male and female scholarship athletes at her university. After comparing the mean GPA of males with the mean GPA of females, she reported no significant difference between the means (p-value = 0.287). What is a correct interpretation of this p-value in the context of the problem?​​​​​​​

  1. The probability that the mean GPA of all male athletes equals the mean GPA of all female athletes is 0.287.
  2. The probability that the mean GPA of all male athletes differs from the mean GPA of all female athletes is 0.287.
  3. If the mean GPA of all male athletes is the same as the mean GPA for all female athletes, the probability of observing a difference between the sample mean GPA for male athletes and the sample mean GPA for female athletes as large or larger than that observed is 0.287.
  4. The probability that the mean GPA of the sample of male athletes differs from the mean GPA of the sample of female athletes is 0.287.

Using the confidence interval (3.546, 6.254), what would be the correct decision to make for the test of hypotheses with H0: μY = μS vs. Ha: μY ≠ μS at α = 0.05?​​​​​​​

  1. Because 0 is not included in the interval, we fail to reject the null hypothesis that the means are equal.
  2. Because 0 is included in the interval, we fail to reject the null hypothesis that the means are equal.
  3. Because 0 is not included in the interval, we reject the null hypothesis and conclude that the means are different.
  4. Because 0 is included in the interval, we reject the null hypothesis and conclude that the means are different.
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