Question

Use the given statistics to complete parts (a) and (b). Assume that the populations are normally distributed. (a) Test whether mu 1greater thanmu 2 at the alphaequals0.05 level of significance for the given sample data. (b) Construct a 90% confidence interval about mu 1minusmu 2. Population 1 Population 2 n 20 23 x overbar 50.7 46.9 s 4.8 12.8 (a) Identify the null and alternative hypotheses for this test. A. Upper H 0: mu 1not equalsmu 2 Upper H 1: mu 1equalsmu 2 B. Upper H 0: mu 1equalsmu 2 Upper H 1: mu 1not equalsmu 2 C. Upper H 0: mu 1greater thanmu 2 Upper H 1: mu 1equalsmu 2 D. Upper H 0: mu 1equalsmu 2 Upper H 1: mu 1less thanmu 2 E. Upper H 0: mu 1less thanmu 2 Upper H 1: mu 1equalsmu 2 F. Upper H 0: mu 1equalsmu 2 Upper H 1: mu 1greater thanmu 2 Your answer is correct. Find the test statistic for this hypothesis test. nothing (Round to two decimal places as needed.)

**Need P-Value**

**Conclusion for this hypothesis test**

**And the answer for part B**

Answer #1

a)

Ho : µ1 = µ2

Ha : µ1 > µ2

Sample #1 ---->

mean of sample 1, x̅1= 50.70

standard deviation of sample 1, s1 =
4.8

size of sample 1, n1= 20

Sample #2 ---->

mean of sample 2, x̅2= 46.900

standard deviation of sample 2, s2 =
12.80

size of sample 2, n2= 23

difference in sample means = x̅1-x̅2 =
50.700 - 46.9000 =
3.8000

std error , SE = √(s1²/n1+s2²/n2) =
2.8767

t-statistic = ((x̅1-x̅2)-µd)/SE = ( 3.8000
/ 2.8767 ) **=
1.32**

**p-value = 0.0986 [excel
function: =T.DIST.RT(t stat,df) ]
Conclusion: p-value>α , Do not reject null
hypothesis **

There is not enough evidence to conclude that µ1 is greater than µ 2

**b)**

α=0.10

Degree of freedom, DF=
28

t-critical value = t α/2 =
1.701 (excel formula =t.inv(α/2,df)

std error , SE = √(s1²/n1+s2²/n2) =
2.877

margin of error, E = t*SE = 1.701
* 2.877 = 4.8937

difference of means = x̅1-x̅2 = 50.7000
- 46.900 = 3.8000

confidence interval is

Interval Lower Limit = (x̅1-x̅2) - E =
3.8000 - 4.894
**= -1.0937**

Interval Upper Limit = (x̅1-x̅2) + E =
3.8000 - 4.894
**= 8.6937**

**===============================**

**please revert for doubts**

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