A boot making company produces women’s cowboy boots. The boots come in either square toe or...

A boot making company produces women’s cowboy boots. The boots come in either square toe or round toe options. In an effort to estimate the proportion of boots sales at their Calgary locations that are square toe, a random sample of 140 boot sales was collected. It was discovered that 65 sales were for square toe boots. Construct a 98% confidence interval to estimate the proportion of Calgarians who purchase square toe boots. Keep 3 decimal places for all calculated values.

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Expert Solution

Solution :

Given that,

n = 140

x = 65

Point estimate = sample proportion = = x / n = 65/140=0.464

1 - = 1- 0.464 =0.536

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Z/2 = Z0.01 = 2.326 ( Using z table )

Margin of error = E = Z / 2 *( $\sqrt$ (( * (1 - )) / n)

= 2.326 ( $\sqrt$ ((0.464*0.536) /140 )

E = 0.098

A 98% confidence interval for population proportion p is ,

- E < p < + E

0.464-0.098 < p <0.464+ 0.098

0.366< p < 0.562

The 98% confidence interval for the population proportion p is : 0.366, 0.562

orchestra answered 11 months ago

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