Consider the following problem statement:

An article in an online magazine states that 40% of home buyers found their real estate agent through referrals by a friend. However, a professor in a local college sampled 1000 home buyers and found that 426 chose an agent recommended by a friend.

Does the data refute the claim made by the magazine? Use a significance level of 0.02.

Solution:

 

Read critical value of z, zα/2  (sometimes shown as z0 ), = -2.33 and +2.33. The rejection regions are in the white areas to the left (less than) -2.33 and to the right (greater than) +2.33.

 

Because the null is our claim, we conclude: There is insufficient evidence to reject the claim that the proportion of home buyers who find their agents from referrals from friends is 40%.

The results are essentially the same as those of Excel’s.

Remember if you are using StatCrunch, you can quickly get the confidence interval around the sample proportion by clicking on the Options button in the upper left of the output box, click Edit, then select the radio button next to Confidence interval for p, and click Compute!

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