Question

Hypothesis Test for a Populatio X G Commute times in the US are + ourse/a2/test/assessement/deliver?contextub4focec30a0001dc699ac1b7bb3531eb&attempt=1 Countdown: Days:-o Time:-03:07:15 Your answer should be rounded to 4 decimal places. Question 16 Child Health and Development Studies (CHDS) has been collecting data about type numbers in the boxes expectant mothers in Oakland, CA since 1959. One of the measurements taken 10 points by CHDS is the weight increase in pounds) for expectant mothers in the second trimester. In a fictitious study, suppose that CHDS finds the average weight increase in the second trimester is 14 pounds. Suppose also that, in 2015, a random sample of 36 expectant mothers have mean weight increase of 15.7 pounds in the second trimester, with a standard deviation of 5.8 pounds. A hypothesis test is done to see if there is evidence that weight increase in the second trimester is greater than 14 pounds. Find the p-value for the hypothesis test. The p-value should be rounded to 4 decimal places,

Answer 1

The sample information is

X = 15.7, S = 5.8, n = 36

we have to test if the mean weight increase in the second trimester is greater than 14pounds

Hence we will conduct a t-test for mean since the population standard deviation is not mentioned in the question.

We will take the significance level =

g= 0,05

(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: 4 = 14 Ha: u > 14 This corresponds to a right-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used. (2) Rejection Region Based on the information provided, the significance level is a = 0.05, and the critical value for a right-tailed test is te = 1.69. The rejection region for this right-tailed test is R=t:t > 1.69 (3) Test Statistics The t-statistic is computed as follows: X-HO 15.7 - 14 t= | s/n 5.8/ 5 =1.759 (4) Decision about the null hypothesis Since it is observed that t = 1.759 >te = 1.69, it is then concluded that the null hypothesis is rejected. Using the P-value approach: The p-value is p=0.0437, and since p=0.0437 < 0.05, it is concluded that the null hypothesis is rejected.

The P value is 0.0437

Since the null hypothesis is rejected we have evidence that the mean weight increase in the second trimester is greater than 14pounds