Question

The time required to start a​ business, defined as the number of days needed to complete the procedures to legally operate a​ business, in 20 developed countries and 20 emerging countries is included in the accompanying table. Complete parts​ (a) through​ (d) below.

DEVELOPED COUNTRIES (DAYS)

24 34   

115 11

7 17

33 20

7 30

4 13

27 10

8 26

6 18

10 22

EMERGING COUNTRIES (DAYS)

2 28

28 15

4 17

5 12

12 5

8 23

15 14

7 8

23 1

2 10

PART A

Assuming that the population variances for developed countries and emerging countries are​ equal, is there evidence of a difference in the mean time required to start a business between developed countries and emerging​ countries? (Use a = 0.05) Let m1 be the mean time required to start a business in developed countries and let m2 be the mean time required to start a business in emerging countries.

the null hypothesis is Ho: m1 = m2

the alternative hypothesis is H1: m1 is not equal to m2

what is the test statistic?

what are the critical values?

state the conclusion?

a- reject ho there is sufficient evidence

b- reject ho there is insufficient evidence

c- do not reject ho there is sufficient evidence

d- do not reject ho there is insufficient evidence

part b

determine the p value?

interpret the meaning

a- the p value is the probability of 2 samples, one taken from each of the two populations , have a mean differnece greater than or equal to the mean difference of these two samples there is no difference in the true population means

b- the p value is the probability that the null hypotheisis is true

c-the p value is the probability of 2 samples, one taken from each of the two populations, have a mean difference less than or equal to the mean difference of these two samples there is a difference in the true population means

d-the p value is the probability of 2 samples, one taken from each of the two populations, have a mean difference equal to the mean difference of these two samples

part c

in addition to equal variance what other assumption is necessary in a ?

a- the two populations have equal standard deviations

b-the two sample sizes are equal

c- the hypothesis test must be a two tail test so the results can be validly compared to a 95% confidence interval

d- the two populations are normally distributed

part d

construct a 95% interval estimate of the difference betweeen the populations mean of developed countries and emerging countries

blank is less thsn or equal to m1- m2 which is less than or equal to blank

Answer 1

In order to solve this question I used R software.

R codes and output:

> d=read.table('data.csv',header=T,sep=',')

> head(d)

    X Y

1 24 2

2 115 28

3   7 4

4 33 5

5   7 12

6   4 8

> attach(d)

The following objects are masked from d (pos = 3):

   X, Y

> t.test(X,Y,var.equal = T)

            Two Sample t-test

data: X and Y

t = 1.7966, df = 38, p-value = 0.08035

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

-1.286978 21.586978

sample estimates:

mean of x mean of y

    22.10     11.95

Test statistic, t = 1.7966

Critical value = 2.024

Conclusion:

Do not reject h0, there is insufficient evidence.

Part B

p-value = 0.08035

the p value is the probability of 2 samples, one taken from each of the two populations , have a mean difference greater than or equal to the mean difference of these two samples there is no difference in the true population means.

Part c

the two populations are normally distributed

Part d.

95% confidence interval for difference between the population mean of developed countries and emerging countries is ( -1.286978 , 21.586978 )