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On pages 6 and 8 of your Stat 200 notebook (Fall 2017 edition), you are computing the power of testing if Talia is a baby genius. In this problem, we imagine that a test was actually performed and your job is to determine if Talia was a baby genius based on the test result. Although some of the calculations here can be done using a regular calculator, you should do all your calculations using R. Store your calculations to variables. This way you don't have to worry about rounding error.
The problem is about testing the hypothesis that Talia is a baby genius. Suppose we asked Talia 100 yes/no questions and she answered 55 questions correctly.
Null hypothesis H0: We'd expect Talia to only get 50% correct. The standard error of the percentage is SE% = 5% as explained in class.
Alternative hypothesis HA: We believe Talia's true ability is 60%. The standard error of the percentage is SE% ≈ 5% as explained in class.
a. Now she got 55% of the correct answers. Assume H0 is true. Convert this percentage to a Z score.
Z0 =
b. Assume H0 is true. Use the normal approximation to calculate the probability that Talia got 55% or more correct answers. Enter your answer to 4 decimal places.
P(≥ 55% | H0) =
c. Assume that HA is true. Use the normal approximation to calculate the probability that Talia got 55% or less correct answers? Enter your answer to 3 decimal places.
P(≤ 55% | HA) =
d. Based on the null cut-off α = 5%, what do you conclude? reject H0: the test result suggests that Talia wasn't answering the questions by random guessing. do not reject H0: not enough evidence to support Talia is a baby genius.
