A research company desires to know the mean consumption of milk per week among m
ID: 3182500 • Letter: A
Question
A research company desires to know the mean consumption of milk per week among males over age 25. A sample of 600 males over age 25 was drawn and the mean milk consumption was 2.8 liters. Assume that the population standard deviation is known to be 1.2 liters. construct the 98% confidence interval for the mean consumption of milk among males over age 25. Answer dearly all parts and show your work. Find the critical value that should be used in constructing the confidence interval. Calculate the margin of error E. Construct the 98% confidence interval.Explanation / Answer
Solution :-
In hypothesis testing, a critical value is a point on the test distribution that is compared to the test statistic to determine whether to reject the null hypothesis. If the absolute value of your test statistic is greater than the critical value, you can declare statistical significance and reject the null hypothesis. Critical values correspond to , so their values become fixed when you choose the test's .
As given in the question, that confidence interval is 98% .
To find the critical value, follow these steps.
b) Margin of error
To compute the margin of error, we need to find the critical value and the standard error of the mean. To find the critical value, we take the following steps.
Next, we find the standard error of the mean, using the following equation:
SEx = s / sqrt( n ) = 1.2 / sqrt( 600 ) = 0.048989
And finally, we compute the margin of error (ME).
ME = Critical value x Standard error = 2.33 * 0.048989 = 0.11414
This means we can be 98% confident that the mean grade point average in the population is 2.8 plus or minus 0.011414, since the margin of error is 0.011414.
c) Constructing 98% confidnce interval
CI for Mean, 2.686 < µ < 2.914
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