Question

The Graduate Management Admission Test (GMAT) is taken by individuals interested in pursuing graduate management education. GMAT scores are used as part of the admissions process for more than 6100 graduate management programs worldwide. The mean sore for all test?takers is 550 with a standard deviation of 120. A researcher in the Philippines is concerned about the performance of undergraduates in the Philippines on the GMAT. She believes that the mean scores for this year's college seniors in the Philippines who are interested in pursuing graduate management education will be less than 550. She has a random sample of 250 college seniors in the Philippines interested in pursuing graduate management education who plan to take the GMAT. Suppose we know that GMAT scores are Normally distributed with standard deviation ?=120. The null and alternative hypotheses are H0:?=550 versus Ha:?<550.

(a) One sample of 250 students had a mean GMAT score of x??=542. Enter this x?? along with the other required information into the P?value of a Test of Significance applet . What is the P?value? (Enter your answer rounded to four decimal places.)

P?value=

Select the correct statement that answers whether the outcome is statistically significant at the ?=0.05 and the ?=0.01 level.

The P?value is not significant at either ?=0.05 or ?=0.01.

The P?value is significant at both ?=0.05 and ?=0.01.

The P?value is significant at ?=0.05 but not at ?=0.01.

The P?value is not significant at ?=0.05 but is significant at ?=0.01.

(b) Another sample of 250 students had x??=532. Use the applet to find the P?value for this outcome. (Enter your answer rounded to four decimal places.)

P-value=

Select the correct statement that answers whether the outcome is statistically significant at the ?=0.05 and the ?=0.01 level.

The P?value is significant at both ?=0.05 and ?=0.01.

The P?value is significant at ?=0.05 but not at ?=0.01.

The P?value is not significant at ?=0.05 but is significant at ?=0.01.

The P?value is not significant at either ?=0.05 or ?=0.01.

(c) Select the statement that correctly explains why these P?values tell us that one outcome is strong evidence against the null hypothesis and that the other outcome is not.

The P?value tells us the probability the null is true. We should expect the P?value to get larger the farther the observed sample mean is from ?=550.

If ?<550, that is if Ha were true, observing values such as 542 or 532 would not be surprising since they are both less than 550, which provides strong evidence that ?<550.

If ?=550, that is if H0 were true, observing a value similar to 542 would not be too surprising, but observing 532 is not very likely at all, which provides strong evidence that ?<550.

Since the P?value is smaller for a sample mean of 542 but bigger for a sample mean of 532, this proves that H0:?=550 is not true.

Answer 1

a) n=250 and

The test statistic:

P-value: 0.146(One tail)

The P?value is not significant at either ?=0.05 or ?=0.01. Because p-value is greater than 0.05 and 0.01

b) n=250 and

The test statistic:

P-value= 0.009

The P?value is significant at both ?=0.05 and ?=0.01. Because P-value is less than 0.005 and 0.01.

c) If ?=550, that is if H0 were true, observing a value similar to 542 would not be too surprising, but observing 532 is not very likely at all, which provides strong evidence that ?<550.