Question

Five hundred draws are made at random with replacement from a box of numbered tickets; 276 are positive. Someone tells you that 50% of the tickets in the box show positive numbers. Do you believe it? Answer yes or no, and explain.

Answer 1

Answer:

No. we cannot believe it as per hypothesis test done.

Step-by-step explanation:

Given that five hundred draws are made at random with replacement from a box of numbered tickets; 276 are positive.

To test the claim whether the proportion for positive numbers is 50% let us conduct a hypothesis test for proportions.

$H_0: p =0.5\\H_a: p\neq 0.5$

(Two tailed test at 5% significance level)

Sample proportion p = $\frac{276}{500} =0.552$

Std error of p = $\sqrt{\frac{P(1-P)}{500} } \\=0.02236$

(assuming null hypothesis to be true)

Here P = 0.50

Test statistic = p difference/std error = $\frac{0.052}{0.02236} \\=2.33$

Z test is used for this proportion.

p value = 0.0198

Since p value <0.05 we reject null hypothesis

At 95% confidence level, there is statistical evidence to show that sample mean is not 50%