The creators David Benioff and D. B. Weiss of the TV show “Game of Thrones”, want...

The creators David Benioff and D. B. Weiss of the TV show “Game of Thrones”, want to know how popular Season 8 was among the show’s fans. They hired an analyst who collected a random sample of 40,106 Game of Thrones fans, and found that 8,156 of those fans said that they like Season 8.

Using this data, the analyst wants to estimate the actual proportion of fans who like Season 8.

What is the lower bound for a 90% confidence interval? Give your answer to 4 decimal places.

Solutions

Expert Solution

n = 40106

x = 8156

= x / n = 8156 / 40106 =0.203

1 - = 1 - 0.203 = 0.797

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645

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

= 1.645 * ( $\sqrt$ ((0.203 * 0.797) / 40106)

= 0.0033

A 90% confidence interval for population proportion p is ,

- E < P < + E

0.203 - 0.0033 < p < 0.203 + 0.0033

0.1997 < p < 0.2063

(0.1997,0.2063)

The 90% confidence interval Lower bound = 0.1997

orchestra answered 1 year ago

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