Question

In: Statistics and Probability

3) In a survey of 517 music teachers, 403 said that the video games Guitar Hero...

3) In a survey of 517 music teachers, 403 said that the video games Guitar Hero and Rock Band have a positive effect on music education. Construct a 98% confidence interval for the proportion of music teachers who believe that these video games have a positive effect. Write a sentence that interprets this interval

Expert Solution

Solution :

Given that,

n = 517

x = 403

Point estimate = sample proportion = = x / n = 403/517=0.779

1 - = 1- 0.779 =0.221

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 ( $\sqrt$ ((0.779*0.221) /517 )

= 0.042

A 98% confidence interval for the proportion is

- E < p < + E

0.779-0.042 < p <0.779+0.042

0.737< p < 0.821

98% confidence interval for the proportion of music teachers who believe that these video games have a positive effect is

(0.737 , 0.821)

lower bound 0.737

upper bound 0.821

orchestra answered 2 years ago

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