Mathematics, 24.03.2020 16:42 harlem3166

Trader Moe’s is considering opening a Fayetteville location but their development office has learned that a main competitor, The Whole Market, currently has a store in development here. Trader Moe’s conducts a survey to see which store shoppers would choose if both were available within a 5 mile radius. Out of 200 shoppers surveyed, 73 would go to Trader Moe’s. Assunming the 95% confidence interval for those who would choose Trader Moe’s. What would happen to the confidence interval if a 99% confidence level were used?

Answers: 1

Show answers

Answers

Answer from: kseniyayakimov

95% confidence

$0.365 - 1.96\sqrt{\frac{0.365(1-0.365)}{200}}=0.298$

$0.365 + 1.96\sqrt{\frac{0.365(1-0.365)}{200}}=0.432$

The 95% confidence interval would be given by (0.298;0.432)

99% confidence

$0.365 - 2.58\sqrt{\frac{0.365(1-0.365)}{200}}=0.277$

$0.365 + 2.58\sqrt{\frac{0.365(1-0.365)}{200}}=0.453$

The 99% confidence interval would be given by (0.27;0.453)

So we can conclude that the 99% confidence interval is wider compared to the 95% interval

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".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

The estimated proportion for this cae is given by:

$\hat p =\frac{73}{200}=0.365$

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:

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

The confidence interval for the mean is given by the following formula:

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

If we replace the values obtained we got:

$0.365 - 1.96\sqrt{\frac{0.365(1-0.365)}{200}}=0.298$

$0.365 + 1.96\sqrt{\frac{0.365(1-0.365)}{200}}=0.432$

The 95% confidence interval would be given by (0.298;0.432)

For the 99% confidence interval, 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:

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

If we replace the values obtained we got:

$0.365 - 2.58\sqrt{\frac{0.365(1-0.365)}{200}}=0.277$

$0.365 + 2.58\sqrt{\frac{0.365(1-0.365)}{200}}=0.453$

The 99% confidence interval would be given by (0.27;0.453)

So we can conclude that the 99% confidence interval is wider compared to the 95% interval

Answer from: Quest

false

step-by-step explanation:

Answer from: Quest

the highest percentage for deaths in construction from highest to lowest is as follows: falls, struck by objects, electrocution, and caught-in/between. these four are collectively known as fatal four.

in the case of falls, the type that is responsible for the overall highest death in the category is falls from roofs.

Another question on Mathematics

Mathematics, 21.06.2019 16:40

Which of the following is most likely the next step in the series? a3z, b6y, c9x, d12w, е15v, f18u

Answers: 2

Answer

Mathematics, 21.06.2019 16:50

An angle that measures between 90 and 180° is called a(,

Answers: 2

Answer

Mathematics, 21.06.2019 18:30

This is my question~~ ( r ^ 4 - 2r ^ 3 - 23 r ^ 2 - 4r - 32)÷(r+4) ~~ i must use long division to solve it : / i was wondering if anyone world like to solve it. and if so, share step-by-step explanations! you! ❤

Answers: 2

Answer

Mathematics, 21.06.2019 20:30

Cody was 165cm tall on the first day of school this year, which was 10% taller than he was on the first day of school last year.

Answers: 1

Answer

You know the right answer?

Trader Moe’s is considering opening a Fayetteville location but their development office has learned...

Questions