Final answer:
Without the standard deviation or test statistic/p-value, we cannot determine whether the class's mean family size is greater than the national average of 3.18. A hypothesis test is needed with the 0.05 level of significance to conclude if we should reject the null hypothesis and affirm the alternative hypothesis that the class's mean is indeed greater.
Step-by-step explanation:
To answer whether the class's mean family size is greater than the national average, we first calculate the sample mean of the family sizes given for the college math class. Adding the family sizes 5, 4, 5, 4, 4, 3, 6, 4, 3, 3, 5, 5, 6, 3, 3, 2, 7, 4, 5, 2, 2, 2, 3, 2 and then dividing the sum by the number of family sizes (which is 24 in this case) gives us the sample mean. We compare this to the national average of 3.18 using a hypothesis test.
To perform a hypothesis test, we would set up our null hypothesis (H0) as the class's mean family size being equal to or less than the national average, and the alternative hypothesis (H1) as the class's mean family size being greater than 3.18. Using a 0.05 level of significance, we would compute the test statistic and compare it to the critical value or compute a p-value and compare it to our alpha to make a decision.
The hypothesis test results are important; if we find that the p-value is less than 0.05, we reject the null hypothesis, which supports the alternative claim that the class's mean family size is greater. However, without the standard deviation and test statistic or p-value, we can't make a definitive decision and answer the question accurately. Therefore, additional information is required to complete this analysis.
If the question had provided the standard deviation or the p-value, detailed steps would be provided to calculate the test statistic or interpret the p-value, which would lead to a conclusion about whether to reject the null hypothesis or not.
The complete question is .....According to the; N.Y. Times Almanac; the mean family size in the U.S. is 3.18. A sample of a college math class resulted in the following family sizes:; At; α; = 0.05 level, is the class’ mean family size greater than the national average? Does the Almanac result remain valid? Why?
a) Yes, at α = 0.05, the class' mean family size is greater than the national average, and the Almanac result remains valid.
b) No, at α = 0.05, the class' mean family size is not greater than the national average, and the Almanac result does not remain valid.
c) Yes, at α = 0.05, but the significance is marginal.
d) No, at α = 0.05, but the significance is marginal......../;