Answered

Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

Anas wants to build a one-sample z interval with 85% confidence to estimate what proportion of users will click an advertisement that appears on his website. He takes a random sample of 250 users and finds that 54 of them clicked the advertisement. Answer the following:

1. What critical value z start superscript, times, end superscript should Anas use to construct this confidence interval?

2. Provide the value of margin of error.

3. Provide the confidence interval with 85% of confidence.

4. What would happen if Anas managed to have 500 sample size?

Sagot :

Answer:

See below

Step-by-step explanation:

Check One Sample Z-Interval Conditions

Simple Random Sample? √

np≥10? √

n(1-p)≥10? √

One-Sample Z-Interval Information

  • Formula --> [tex]CI=\hat{p}\pm z^*\biggr(\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\biggr)[/tex]
  • Sample Proportion --> [tex]\hat{p}=\frac{54}{250}=0.216[/tex]
  • Critical Value --> [tex]z^*=1.4395[/tex] (for a 85% confidence level)
  • Sample Size --> [tex]n=250[/tex]
  • Margin of Error (MOE) --> [tex]\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]

Problem 1

As stated previously, Anas should use the critical value [tex]z^*=1.4395[/tex] to construct the 85% confidence interval

Problem 2

Given our formula for the margin of error (MOE), the value is [tex]MOE=\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=\sqrt{\frac{0.216(1-0.216)}{250}}\approx0.026[/tex]

Problem 3

The 85% confidence interval would be [tex]CI=\hat{p}\pm z^*\biggr(\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\biggr)=CI=0.216\pm 1.4395(0.026)\appro=\{0.1786,0.2534\}[/tex], which means that we are 85% confident that the true proportion of people that clicked on the advertisement is between 0.1786 (~45 people) and 0.2534 (~63 people)

Problem 4

Increasing the sample size to [tex]n=500[/tex] is going to decrease the margin of error because it is a closer representation of the population, but, alas, requires more time, energy, and resources to observe.

Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.