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.

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.

(Two tailed test at 5% significance level)

Sample proportion p =

Std error of p =

(assuming null hypothesis to be true)

Here P = 0.50

Test statistic = p difference/std error =

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%

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