Question

To test Ho: u = 105 versus Hy: # 105 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? O A. No, because the test two-tailed OB. Yes, because n 2 30. OC. No, because n 2 30. OD. Yes, because the sample random (b) If x= 101.9 and s=5.8, compute the test statistic. The test statistic is to - (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 A. ОВ. Oc. a Q @ (d) Approximate the P-value. Choose the correct answer below. O A. 0.01 <P-value < 0.02 OB. 0.002 < P-value < 0.005 OC. 0.005 < P-value < 0.01 OD. 0.001 <P-value < 0.002 Interpret the P-value. Choose the correct answer below. O A. If 1000 random samples of size n = 35 are obtained, about 3 samples are expected to result in a mean as extreme or more extreme than the one observed if u = 105. OB. If 100 random samples of size n= 35 are obtained, about 3 samples are expected to result in a mean as extreme or more extreme than the one observed if u = 105. OC. If 1000 random samples of size n= 35 are obtained, about 3 samples are expected to result in a mean as extreme or more extreme than the one observed if u = 101.9. OD. If 1000 random samples of size n= 35 are obtained, about 10 samples are expected to result in a mean as extreme or more extreme than the one observed if u = 105. (e) If the researcher decides test this hypothesis at the a = 0.05 level of significance, will the researcher reject the null hypothesis? Yes о No

Answer 1

Given
X bar	101.9
μ0	105
S	5.8
n	35

a)

No, because n >= 30

Hypothesis :		α=	0.05
		df	34	n-1
Ho:	μ​ = μ0
Ha:	μ​ not = μ0	Two tailed
t Critical Value :
tc	2.032244509	T.INV.2T(alpha,df)	TWO
Rejection region:
ts	< for -	tc	TWO	To reject
ts	> for +	tc	TWO	To reject
b)Test :
ts	-3.16	(X bar-μ )/(S/SQRT(n))
P value :
P value	0.003288849	T.DIST.2T(-ts,df)	TWO
Decision :
P value	<	α	Reject H0

c)

B. Q

d)

P value = 0.0033

0.002 < P value < 0.005

OD. If 1000 random samples of size n = 35 are obtained, about 3 samples are expected to result in a mean as extreme or more extreme than the one observed if u = 105.

e)

P value < 0.05, Reject H0