7. (10 pts.) The national mean score for the SAT is 910. An SAT preparation program claims that, on average, its graduates score higher than the national average of 910. To test the program’s claim, 36 students who have applied to take the SAT are selected randomly for inclusion in the prep course.
anwsers must be in 4 decimal places
a. What are the hypotheses for the test?
b. Let X be the SAT score of a graduate of the prep
program. Describe the distribution of the sample mean for samples
of 36 students under the null hypothesis. You must address its
shape, mean and spread. Sketch and label the distribution.
c. The mean SAT score for the 36 students selected
turns out to be 943. Assuming the standard deviation for the SAT
scores is known to be , find the P-value for the test you described
in part (a).
aClaim is that average graduates score is higher than 910 but null hypothesis always has an equality sign so the claim is alternate hypothesis
.
b.As the n=36>30 according to Central Limit theorem the distribution is normal and bell shaped
c.As n is sufficient large and population standard deviation is known we will use z distribution.
P=value for P(z>2.64) for one tailed test is 0.0041
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