Hypothesis Testing Onesample test In a test of ten truefals

Hypothesis Testing – One-sample test

In a test of ten true-false questions, Hermione got 8 correct. Test at 5% significance level whether the proportion of correct answers she has obtained is significantly higher than what would be expected by randomly guessing all the answers.

Solution

True or false question

Hence prob for correct guessing =0.5

X no of correct questions is binomial with p = 0.5 and n = 8

Mean = np = 4

Var = npq = 2

H0: x bar = 4

Ha: xbar > 4

Right tailed test

Test statistic = (8-4)/rt 2

= 2 rt 2

= -2.828

p value =0.0024

As p < 0.01, reject null and accept alternate

the proportion is sign. higher