jwescantrell
Answered

At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay $100 for the upgrade. For the upgrade to be profitable, the company needs to sell it to more than 25% of its customers. You contact a random sample of 72 customers and find that 19 would be willing to pay $100 for the upgrade.

a) Do the sample data give good evidence that more than 25% of the company’s customers are willing to purchase the upgrade? Carry out an appropriate test at the α = 0.05 significance level. (You must include all of the steps of the STATE, PLAN, DO, CONCLUDE method to earn full credit.)

b) Describe in context the consequence if we commit a Type II error in this case.

Sagot :

batolisis

A)  The critical value at α = 0.05  will be 1.645 since the critical value does not fall within the rejection region we reject the null hypothesis

B) A type II error occurs when we fail to reject the null hypothesis and a type II error is also known as an error of omission and the consequence of this type of error is that a false negative result is produced.

Given data :

Amount paid for upgrade = $100

Percentage of customers needed  = 25% = 0.25

Sample size ( n ) = 72

Number willing to pay $100 = 19

significance level ( α ) = 0.05

A) Prove that 25% of the company's customers are willing to purchase the upgrade

Null hypothesis ( H0 ) : p = 0.25

Alternate hypothesis ( H₁ ) : p > 0.25

α  = 0.05

Ρ = 19 / 72 = 0.26

To determine the hypothesis to reject or accept

perform Test statistic :  Z = [tex]\frac{P - p }{\sqrt{\frac{p(1-p)}{n} } }[/tex]  

                                          = ( 0.26 - 0.25 ) / [tex]\sqrt{0.25 * 0.75} / 72[/tex]

                                          = 0.01 / 0.0026

                                      Z- score = 0.499

The critical value at α = 0.05  will be 1.645 since the critical value does not fall within the rejection region we reject the null hypothesis

B)  A type II error occurs when we fail to reject the null hypothesis and a type II error is also known as an error of omission and the consequence of this type of error is that a false negative result is produced.

Learn more about Type II error : https://brainly.com/question/7278657?section=related_q

We hope this was helpful. Please come back whenever you need more information or answers to your queries. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.