Question

An administrator at a college claims that the mean SAT Mathematics score of incoming students is 520. You find that in a random sample of 45 incoming students, the mean SAT Mathematics score is 511 with a standard deviation of 48.65. Assume the population of scores are normally distributed.  

Suppose you perform a hypothesis test to determine whether the mean SAT Mathematics score of incoming students is less than 520.

What is the P-value for this hypothesis test? Round the value to two decimal places.

Answer 1

Solution :

The null and alternative hypothesis are

H₀ : $\mu$ = 520   ........... Null hypothesis

H_a : $\mu$ < 520   ........... Alternative hypothesis

Here,  n = 45, $url=http://latex.codecogs.com/gif.latex?%5Cbar%20x&t=1596143374&ymreqid=69d777f6-ff7f-1f97-1ce8-d7000001af00&sig=ywyOQiGOzvBxFtgft_NhSg--~D$ = 511, s = 48.65

The test statistic t is,

t =  

T-]/[s/n

= [511 - 520]/[48.65 /$\sqrt{}$45]

= -1.24

The value of the test​ statistic t = -1.24

Now ,

d.f. = n - 1 = 45 - 1 = 44

< sign in Ha indicates that the test is ONE TAILED.

t = -1.24

So , using calculator ,

p value = 0.1108

Answer : The P-value for this hypothesis test is 0.11