ISLETME ve YÖNETIM BILIMLERI FAKÜLTESi FACULTY OF BUSINESS AND ADMINISTRATIVE SC

Question

ISLETME ve YÖNETIM BILIMLERI FAKÜLTESi FACULTY OF BUSINESS AND ADMINISTRATIVE SCIENG ES A researcher is interested in profitability of manufacturing and construction firms s is 14min liras with standard error of 2min Liras. a. Test the null hypothosis that variations of profitability are the same takes a random sample of 15 manufacturing and 10 construction firms, and founds that average firms is 10min Liras with standard error of 3min Liras whereas average profitability of firm manufactur arvd both in construction industries. (8p) b. Test the null hypothesis that both industries have the same profitability at 5% significance level. (12p) Baarnlar Dileriz/Good L

Explanation / Answer

n1 =15 , n2 = 10

s1 = 3 , s2 = 2

Xbar 1 =10 Xbar2 = 14

a)

Test and CI for Two Variances

Method

Null hypothesis         (First) / (Second) = 1
Alternative hypothesis (First) / (Second) 1
Significance level      = 0.05

F method was used. This method is accurate for normal data only.

Statistics

                               95% CI for
Sample   N StDev Variance      StDevs
First   15 3.000     9.000 (2.196, 4.731)
Second 10 2.000     4.000 (1.376, 3.651)

Ratio of standard deviations = 1.500
Ratio of variances = 2.250

95% Confidence Intervals

                            CI for
         CI for StDev      Variance
Method       Ratio           Ratio
F       (0.770, 2.687) (0.592, 7.221)

Tests

                       Test
Method DF1 DF2 Statistic P-Value
F             14    9       2.25      0.224

p-value = 0.224 > 0.05

hence we fail to reject the null hypothesis

b)

Two-Sample T-Test and CI

Sample   N   Mean StDev SE Mean
1       15 10.00   3.00     0.77
2       10 14.00   2.00     0.63

Difference = (1) - (2)
Estimate for difference: -4.00
95% CI for difference: (-6.07, -1.93)
T-Test of difference = 0 (vs ): T-Value = -4.00 P-Value = 0.001 DF = 22

p-value = 0.001 < 0.05

hence we reject the null hypothesis

and conclude that there is significant difference in profitability

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