Astronauts often report that there are times when they become disoriented as they move around in...

Astronauts often report that there are times when they become disoriented as they move around in zero-gravity. Therefore, they usually rely on bright colors and other visual information to help them establish a top-down orientation. A study was conducted to assess the potential of using color for body orienting. 75 college students, reclining on their backs in the dark, found it difficult to establish orientation when positioned on under a rotating disk. This rotating disk was painted half black and half white. Out of the 75 students, 40 believed they were right side up when the white was on top. Use this information to estimate the true proportion of subjects who use the white color as a cue for right-side-up orientation. That is, construct a 95% confidence interval for the true proportion.

____≤?≤____

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample proportion = = x / n = 40 / 75 = 0.533

1 - = 1 - 0.533 = 0.467

Z_/2 = 1.96

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

= 1.96 * ( $\sqrt$ ((0.533 * 0.467) / 75)

= 0.113

A 95% confidence interval for population proportion p is ,

- E p + E

0.533 - 0.113 p 0.533 + 0.113

0.420 p 0.646

The 95% confidence interval for the population proportion p is : 0.420 , 0.646

orchestra answered 1 year ago

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