Random samples of female and male drivers are asked to estimate the number of mi

Question

Random samples of female and male drivers are asked to estimate the number of miles that each drives in a year. The data is below:

Females (Population 1): 9400, 7800, 9300, 8900, 8600, 9100, 8400, 7800, 8800

Males (Population 2): 10200, 10400, 10500, 9000, 9900, 9700, 8800

Is there evidence, at an =0.1 level of significance, to conclude that there is a difference in the number of miles driven between females and males? Carry out an appropriate hypothesis test, filling in the information requested.

A. The value of the standardized test statistic:

Note: For the next part, your answer should use interval notation. An answer of the form (,a) is expressed (-infty, a), an answer of the form (b,) is expressed (b, infty), and an answer of the form (,a)(b,) is expressed (-infty, a)U(b, infty).

B. The rejection region for the standardized test statistic:

C. Your decision for the hypothesis test:

A. Do Not Reject H1 .
B. Reject H0 .
C. Do Not Reject H0 .
D. Reject H1 .

Explanation / Answer

Random samples of female and male drivers are asked to estimate the number of miles that each drives in a year.

Assume alpha = level of significance = 0.1

Here we use t-test for two samples because sample size is small and population standard deviation is unknown.

Here we have to test the hypothesis that,

H0 : mu1 = mu2 Vs H1 : mu1 mu2

where mu1 is population mean for number of miles drive for females.

and mu2 is population mean for number of miles drive for males.

Here first we have to test whether variances are equal or not.

The hypothesis for the test is,

H0 : Variances are equal.

H1 : Variances are not equal.

All this we can done by using EXCEL.

steps are :

Enter all the data in EXCEL sheet --> DATA --> Data Analysis --> F-Test Two-Sample For Variances --> ok --> Variable 1 Range : select all x-values --> Variable 2 Range : select all y-values --> Alpha = 0.1 --> Output Range : select any empty cell --> ok

Output is,

Test statistic F = 0.780

P-value = 0.3623

P-value > alpha (0.1)

Accept H0 at 0.1 level of significance.

Conclusion : Variances are equal.

So here for testing two means we use pooled variances.

Testing two means using t-test :

EXCEL steps :

DATA --> Data Analysis --> t-Test: Two sample Assuming Equal Variances --> ok --> Variable 1 Range : select all x-values --> Variable 2 Range : select all y-values --> Alpha = 0.1 --> Output Range : select any empty cell --> ok

Output is,

Test statistic t = -3.5255

P-value = 0.003

P-value < alpha (0.1)

Reject H0 at 0.1 level of significance.

Conclusion : Population mean for number of miles drive for females is differ than population mean for that of males.

F-Test Two-Sample for Variances Variable 1 Variable 2 Mean 8677.777778 9785.714286 Variance 346944.4444 444761.9048 Observations 9 7 df 8 6 F 0.780067809 P(F<=f) one-tail 0.362349292 F Critical one-tail 0.374765576

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.