3. Last year, Lipton Tea Company conducted a mall intercept study at six regional malls around the country and found that 20% of the public preferred tea over coffee as a midafternoon hot drink. This year, Lipton wants to have a nationwide telephone survey performed with random digit dialing. What sample size should be used in this year’s study to achieve an accuracy level of ±2.5% at the 99% level of confidence? What about at the 95% level of confidence? (4 points)

a)  

And rounded up we have that n=1705

b)  

And rounded up we have that n=984

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

Solution to the problem

Part a

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by and . And the critical value would be given by:

The margin of error for the proportion interval is given by this formula:  

   (a)  

And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

  (b)  

And replacing into equation (b) the values from part a we got:

And rounded up we have that n=1705

Part b

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by and . And the critical value would be given by:

And rounded up we have that n=984

step- i d k and i d c : )

you: : 0

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