Question

According to a survey of 5041 Star Trek fans conducted in 2010, 2873 are females. Use this data to test the claim that the majority of Star Trek fans are female. Use 0.10 as the significance level.

p-value=0.570, evidence not support claim

p-value=1.000, evidence not support claim

p-value=0.570, evidence support claim

p-value=1.578, evidence not support claim

p-value=0.000, evidence support claim

Answer 1

We need to test the claim that the majority of Star Trek fans are female

So Null Hypothesis H0 : p = 0.5

Alternate Hypothesis H1 : p > 0.5

where p is the proportion of star trek fans that are female

Given According to a survey of 5041 Star Trek fans conducted in 2010, 2873 are females

So Proportion of females who are fans of Star Trek = 2873 / 5041

= 0.569927

Here n = 5041

We will calculate the z-score

Z-score = ( - p ) / p * (1 - p) / n

= (0.569927 - 0.5) / 0.5 * 0.5 / 5041

= 0.069927 / 0.0070442254

= 9.929577

The p-value for a z-score of 9.29577 for a one-tailed test is 0.000 The value was calculated by using calculators since the normal z-tables doesn't have large z-scores

Here we are using one tailed test becuase we are looking for a proportion that is greater than 0.5. If it was just equal to we would have used two-tailed test

SInce the p-value is less than the significance level, we reject the Null Hypothesis and therefore the evidence supports the claim

So Answer is Option E