Question

1) A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Use a 0.10 significance level for both parts.

2) A study was done on body temperatures of men and women. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Use a 0.01 significance level for both parts.

3) Given in the table are the BMI statistics for random samples of men and women. Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Use a 0.01 significance level for both parts.

The test​ statistic, t, is

.

​(Round to two decimal places as​ needed.)

The​ P-value is

.

​(Round to three decimal places as​ needed.)

State the conclusion for the test.

A.

Fail to rejectFail to reject

the null hypothesis. There

isis

sufficient evidence to support the claim that men have a higher mean body temperature than women.

B.

RejectReject

the null hypothesis. There

is notis not

sufficient evidence to support the claim that men have a higher mean body temperature than women.

C.

RejectReject

the null hypothesis. There

isis

sufficient evidence to support the claim that men have a higher mean body temperature than women.

D.

Fail to rejectFail to reject

the null hypothesis. There

is notis not

sufficient evidence to support the claim that men have a higher mean body temperature than women.

b. Construct a confidence interval suitable for testing the claim that men have a higher mean body temperature than women.

less than<mu 1 minus mu 2μ1−μ2less than<

​(Round to three decimal places as​ needed.)

Does the confidence interval support the conclusion of the​ test?

No,Yes,

because the confidence interval contains

Treatment Placebo μι 25 x 2.33 S0.95 μ2 37 2.65 0.68 Men μι 97.55°F 0.96°F Women μ2 59 97.41°F 0.65°F

Answer 1

2)

a)

Ho :   µ1 - µ2 =   0
Ha :   µ1-µ2 >   0

Level of Significance ,    α =    0.01
      
mean of sample 1,    x̅1=   97.55
standard deviation of sample 1,   s1 =    0.96
size of sample 1,    n1=   11
      
mean of sample 2,    x̅2=   97.41
standard deviation of sample 2,   s2 =    0.65
size of sample 2,    n2=   59
      
difference in sample means =    x̅1-x̅2 =    0.1400
      
std error , SE =    √(s1²/n1+s2²/n2) =    0.3016
      
t-statistic =    ((x̅1-x̅2)-µd)/SE =    0.46

DF = min(n1-1 , n2-1 )=   10

p-value=0.326

p-value>α , Do not reject null hypothesis

Fail to reject

the null hypothesis. There

is not sufficient evidence to support the claim that men have a higher mean body temperature than women.

b)

t-critical value =    t α/2 = 3.169 (excel formula =t.inv(α/2,df)
                  
                  
                  
std error , SE =    √(s1²/n1+s2²/n2) =    0.3016          
margin of error, E =    t*SE =    0.9366       0.956
                  
difference of means =    x̅1-x̅2 =    0.1400          

confidence interval is                   
Interval Lower Limit=   (x̅1-x̅2) - E =    -0.816
Interval Upper Limit=   (x̅1-x̅2) + E =     1.096

the confidence interval does not support the conclusion of the​ test

because the confidence interval contains 0 in th the interval