est: Final Exam his Question: 1 pt 3 of 10 (1 complete) | > To test Ho: H 105 ve
ID: 3352201 • Letter: E
Question
est: Final Exam his Question: 1 pt 3 of 10 (1 complete) | > To test Ho: H 105 versus H, H105 a simple random sample of size n- 35 is obtained. Complete parts a through e below click here to view the t Distribution Area in Right Tail (a) Does the population have to be normally distributed to test this hypothesis? Why? A. No, because the test is two-tailed O B. Yes, because the sample is random O C. No, because n 2 30 O D. Yes, because n 230 (b) If x 101.9 and s- 5.8, compute the test statistic. The test statistic ish" (Round to two decimal places as needed ) (c) Draw a t-distribution with the area that represents the P-value shaded. Choose the correct graph below O C. Click to select your answer(s) IO e O Type here to searchExplanation / Answer
Give mu = 105
n = 35
a)
as the sample size is greater than 30 , hence we must have normal distribution of data , so D
b)
xbar = 101.9
s = 5.8
the test stat is given as
t = (xbar-mu)/(sd/sqrt(n)), putting the values
t = (101.9-105)/(5.8/sqrt(35)) = - 3.16
c) as the alternative hypothesis is
mu not equal to 105 , hence this is a 2 tail test so the correct choice is b
d)
now we check the t table to find the p value
degree of freedom is n-1
= 35-1 = 34
and assuming alpha = 0.05 , we see from the t table that
The P-Value is .003486.
hence B , The result is significant at p < .05.
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