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. (Start up incubators hold classes and help startups to contact venture capitalists and network with one another) Assume funding is normally distributed.

Incubator A has a 40% success ratio getting companies to survive at least 4 years from inception. The average venture funding of the 27 companies reaching that 4 year mark, is 1.3 million dollars with a standard deviation of 0.3 million.

Incubator B has a 39% success ratio getting companies to survive at least 4 years from inception. The average venture funding of the 18 companies reaching that 4 year mark, is 1.9 million dollars with a standard deviation of .6 million.

a.) do the standard deviations differ significantly? (use alpha =.01).

b.) Is the average funding in incubator B significantly better? (use alpha=.05)

Explanation / Answer

Part-a

For this we applied f-test of equality of variances and the folowing results showed that we have enough evidence to conclude that variances are signifcantly different as F(26,17)=0.25 , p=0.002<0.05

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 27 0.300 0.090 (0.236, 0.411)
Second 18 0.600 0.360 (0.450, 0.899)

Ratio of standard deviations = 0.500
Ratio of variances = 0.250

95% Confidence Intervals

CI for
CI for StDev Variance
Method Ratio Ratio
F (0.314, 0.764) (0.099, 0.584)

Tests

Test
Method DF1 DF2 Statistic P-Value
F 26 17 0.25 0.002

Part-b

Assuing unequal varianeces we applied two-sample t-test and the following results showed that we have enough evidence to conclude that average funding in incubator B significantly better as t(22)=3.93 , p=0.000<0.05.

Two-Sample T-Test and CI

Sample N Mean StDev SE Mean
1 18 1.900 0.600 0.14
2 27 1.300 0.300 0.058

Difference = (1) - (2)
Estimate for difference: 0.600
95% lower bound for difference: 0.338
T-Test of difference = 0 (vs >): T-Value = 3.93 P-Value = 0.000 DF = 22

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