Question

Question 7 Child Health and Development Studies (CHDS) has been collecting data about Select one answer expectant mothers in Oakland, CA since 1959. One of the measurements taken to 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 40 expectant mothers have mean weight increase of 16 pounds in the second trimester, with a standard deviation of 6 pounds. At the 5% significance level, we can conduct a one-sided T-test to see if the mean weight increase in 2015 is greater than 14 pounds. Statistical software tells us that the p-value = 0.021 Which of the following is the most appropriate conclusion? A. There is a 2.1% chance that a random sample of 40 expectant mothers will have a mean weight increase of 16 pounds or greater if the mean second trimester weight gain for all expectant mothers is 14 pounds. B. There is a 2.1% chance that mean second trimester weight gain for all expectant mothers is 14 pounds in 2015. C. There is a 2.1% chance that mean second trimester weight gain for all expectant mothers is 16 pounds in 2015. D. There is 2.1% chance that the population of expectant mothers will have a mean weight increase of 16 pounds or greater in 2015 if the mean second trimester weight gain for all expectant mothers was 14 pounds in 1959.

Answer 1

In hypothesis testing p-value signifies the acceptance probability of null hypothesis. Say the significance level is alpha ( which we set as low as possible, here it is 5% =0.05). Suppose the test has p-value is p*. We can say that p* is the probability that the null hypothesis is true. We can reject null hypothesis if p* s below alpha.

Here our hypothesis will be

H0: mu=14

Vs

H1: mu>14

Hence, definition of p-value is P( T>tobs ).

Where tobs = observed value of test statistic

Now we have given =p-value =0.021

So we will reject H0 here since p-value <0.05=significance level

The significance will be the chance of being accepted H0 is 2.1%.

That is 2.1% chance of the mean is 14 in 2015 also. Hence option B is correct here.

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