Mathematics, 07.04.2020 16:10 Ashu638

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)

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Answer from: itsyagirlgona21

a) $n=\frac{0.2(1-0.2)}{(\frac{0.025}{2.58})^2}=1704.04$

And rounded up we have that n=1705

b) $n=\frac{0.2(1-0.2)}{(\frac{0.025}{1.96})^2}=983.45$

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 $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58$

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

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.025$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

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

$n=\frac{0.2(1-0.2)}{(\frac{0.025}{2.58})^2}=1704.04$

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 $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

$n=\frac{0.2(1-0.2)}{(\frac{0.025}{1.96})^2}=983.45$

And rounded up we have that n=984

Answer from: Quest

step-by-step explanation:

an equation by definition has to have two or more variables (x and 2 in this case)

Answer from: Quest

0.69 yards

step-by-step explanation:

there are 36 inches in a yard

25 : 36 = 0.69 yards (you can round to 0.70)

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3. Last year, Lipton Tea Company conducted a mall intercept study at six regional malls around the c...