Question

Online magazines make it easy for readers to link to an advertiser’s website directly from an advertisement. A recent survey indicated that 56% of online magazine readers have clicked on the advertisement. The survey was based on a sample size of 6,403.

Determine if there is evidence that more than half of the online readers have clicked on the advertisement at ? = 0.05. You may use the p-value or critical value approach.

Now assume the sample size is 100. Repeat part (a).

Discuss the effect that sample size has on hypothesis testing.

Answer 1

1) with sample size n=6403:

as test statsitic is in critical region we reject null hypothesis

we have sufficient evidence at 0.05 level to conclude that more than half of the online readers have clicked on the advertisement

with sample size n=100

as test statsitic is not in critical region we can not reject null hypothesis

we do have sufficient evidence at 0.05 level to conclude that more than half of the online readers have clicked on the advertisement

here we can see that as sample size decreases the test becomes less significant whcih reflect that bigger sample sizes can make a practically insigniicant effect ; statistically significant or vice versa,