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Enough money has been budgeted to collect independent random samples of size n1=n2=100from populations 1 and 2 to estimate localid="1664867109106" 1-2. Prior information indicates that 1=2=10. Have sufficient funds been allocated to construct a 90% confidence interval for1-2of width 5 or less? Justify your answer.

Short Answer

Expert verified

The required sample size is 22. Since, the sample size for each population is large enough.

Step by step solution

01

Given Information

The sample size of two populations are given below

n1=n2=100

The standard deviation of two populations are given below

1=2=10

The sampling error is

SE=5

02

Z-value

For =0.1

The z-value is given by

z2=z0.05=1.645

03

Compute the sample

For, z=1.645,1=2=10andSE=5

The sample is calculated as

n1=n2=z0.05212+22SE2=1.6452102+10252=2.706020025=541.225=21.64822

Therefore, the required sample size is 22.

Since, the sample size for each population is large enough.

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