Constructing a 95 percent interval?

2014-07-30 9:35 am

In a town, pizza selling rate has been poor and only 5% of townspeople bought
pizza in 2013.  The pizza store wants to increase their selling rate.  It runs a campaign
during the first half of 2014 to increase the popularity of their pizza.
At the end of the campaign, the association randomly samples 500 townsfolk, and finds
that 30 of these people have bought pizza in the past month.  The store will use the data
obtained to determine if the campaign is effective in raising pizza selling rate.

Construct a 95% confidence interval for the parameter of interest.

In this case is p given? I am not quite sure, if it does then it should follow the normal distribution model no? Is it possible to construct a 95 percent interval for a normal model? Do i still have to go through the Standard Error steps?

更新1:

Sorry, i mean confidence interval.

回答 (1)

[匿名]

2014-07-30 9:52 am

The sample proportion is p^=30/500=0.06
The new population proportion is not known so estimate it by 0.06.
The standard deviation of p^ is approximately
√(0.06*0.94/500) ≈0.01062 so the 95% confidence interval is given
by 0.06 - 1.96*0.01062 < p < 0.06+1.96*0.01062
so 0.039 < p < 0.081 correct to 2 SF.

p is not given in the question and you have to use an estimate from
the sample

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