You and a group of friends wish to start a company. You have an idea, and you ar

Question

You and a group of friends wish to start a company. You have an idea, and you are comparing startup incubators to apply to. Assume funding is normally distributed.

Incubator A has a 80% success ratio getting companies to survive at least 4 years from inception. The average venture funding of the 29 companies reaching that 4 year mark, is 1.6 million dollars with a standard deviation of 0.4 million.

Incubator B has a 81% success ratio getting companies to survive atleast 4 years from inception. The average venture funding of the 28 companies reaching that 4 year mark, is 1.8 million dollars with a standard deviation of 0.3 million

a. Do the standard deviations differ significantly? (use alpha=0.1)

b. Is the average funding in incubator B significantly better? (use alpha=0.05)

Explanation / Answer

Part-a

From following results we found that the standard deviations do not differ significantly as F(28,27)=1.78 with p=0.139>0.1

Test and CI for Two Variances

Method

Null hypothesis (First) / (Second) = 1
Alternative hypothesis (First) / (Second) 1
Significance level = 0.1

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

Statistics

90% CI for
Sample N StDev Variance StDevs
First 29 0.400 0.160 (0.329, 0.514)
Second 28 0.300 0.090 (0.246, 0.388)

Ratio of standard deviations = 1.333
Ratio of variances = 1.778

90% Confidence Intervals

CI for
CI for StDev Variance
Method Ratio Ratio
F (0.968, 1.833) (0.937, 3.359)

Tests

Test
Method DF1 DF2 Statistic P-Value
F 28 27 1.78 0.139

Part-b

As standard deviations are not significantly different we applied two-sample t-test assuming equal vairnace and the results showed that  average funding in incubator B significantly better as t(55)= 2.13 with p-value=0.019<0.05

Two-Sample T-Test and CI

Sample N Mean StDev SE Mean
1 28 1.800 0.300 0.057
2 29 1.600 0.400 0.074

Difference = (1) - (2)
Estimate for difference: 0.2000
5% lower bound for difference: 0.3571
T-Test of difference = 0 (vs >): T-Value = 2.13 P-Value = 0.019 DF = 55
Both use Pooled StDev = 0.3545

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