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From a random sample of 100 male students at Hope College, 16 were left-handed. Using the...

From a random sample of 100 male students at Hope College, 16 were left-handed. Using the theory-based inference applet, determine a 99% confidence interval for the proportion of all male students at Hope College that are left -handed. Round your answers to 4 decimal places, e.g. "0.7523.

Expert Solution

Solution :

Given that,

n = 100

x = 16

= x / n = 16 / 100 = 0.16

1 - = 1 - 0.16 = 0.84

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

= 2.576 * ( $\sqrt$ ((0.16 * 0.84) / 100)

= 0.0944

A 99% confidence interval for population proportion p is ,

- E < P < + E

0.16 - 0.0944 < p < 0.16 + 0.0944

0.0656 < p < 0.2256

(0.0656 , 0.2256)

milcah answered 6 months ago

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