Question

A fashion designer wants to know how many new dresses women buy each year. A sample of 523 women was taken to study their purchasing habits. Construct the 95% confidence interval for the mean number of dresses purchased each year if the sample mean was found to be 7.3. Assume that the population standard deviation is 1.4. Round your answers to one decimal place.

Answer 1

The confidence interval for the meannumber of dresses purchased each year is (7.2,7.4).

Given sample mean of 7.3 and sample standard deviation of 1.4 and confidence interval of 95%.

We have to find confidence interval for the mean number of dresses purchased each year.

Because the sample size is more than 30 so z test test will be used.

Margin of error is the difference in real values and calculated values.

Margin of error=z*σ/$\sqrt{n}$

where zis the criticalvalue of confidence level.

σ is sample standard deviation,

n is sample size.

z value for 95% confidence level=1.96

Margin of error=1.96*1.4/$\sqrt{523}$

=2.744/22.869

=0.12

Upper level= Mean + margin of error

=7.3+0.12

=7.42

Rounding off

=7.4

Lower level=Mean - margin of error

=7.3-0.12

=7.18

Rounding

=7.1

Hence the confidence interval is (7.1,7.4).

Learn more about confidence interval at https://brainly.com/question/15712887

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