# MATH225 Week 7 Assignment – Developing Hypothesis and Understanding Possible Conclusions for Proportions

Identify the null and alternative hypotheses for an experiment with one population proportion

Question

Tyler claims that less than 80% of the undergraduate students at his college have at least one sibling. He randomly selects 112 undergraduate students to survey whether they have at least one sibling. Tyler found that 87 of the 112 have at least one sibling. What are the null and alternative hypotheses for this hypothesis test?

{H0:p=0.8Ha:p>0.8

{H0:p≠0.8Ha:p=0.8

{H0:p=0.8Ha:p<0.8

{H0:p=0.8Ha:p≠0.8

Compute the value of the test statistic (z-value) for a hypothesis test for proportion

## Question

A researcher is investigating a government claim that the unemployment rate is less than 5%. To test this claim, a random sample of 1500 people is taken and its determined that 92 people are unemployed.

The following is the setup for this hypothesis test:

{H0:p=0.05 Ha:p<0.05

Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.

Compute the value of the test statistic (z-value) for a hypothesis test for proportion

## Question

A hospital administrator claims that the proportion of knee surgeries that are successful is 87%. To test this claim, a random sample of 450 patients who underwent knee surgery is taken and it is determined that 371 of these patients had a successful knee surgery operation.

The following is the setup for this hypothesis test:

{H0:p=0.87Ha:p≠0.87

Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.

Identify the null and alternative hypotheses for an experiment with one population proportion

## Question

Kylie works for a large nursery and is investigating whether to use a new brand of seeds. The new brand of seeds advertises that 93% of the seeds germinate, which is higher than the germination rate of the seeds she is currently using. She will change over to this new brand unless the actual germination rate is less than what is advertised. Kylie conducts an experiment by randomly selecting 76 seeds of the new brand and plants them. She finds that 70 of those seeds germinated. What are the null and alternative hypotheses for this hypothesis test?

Compute the value of the test statistic (z-value) for a hypothesis test for proportion

## Question

A business owner claims that the proportion of take out orders is greater than 25%. To test this claim, the owner checks the next 250 orders and determines that 60 orders are take out orders.

The following is the setup for this hypothesis test:

{H0:p=0.25Ha:p>0.25

Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.

Compute the value of the test statistic (z-value) for a hypothesis test for proportion

## Question

A college professor claims that the proportion of students passing a statistics course is 80%. To test this claim, a random sample of 250 students who previously took the course is taken and it is determined that 221 students passed the course.

The following is the setup for this hypothesis test:

H0:p = 0.80

Ha:p ≠ 0.80

Find the test statistic for this hypothesis test for a proportion and round your answer to 2 decimal places.

Identify the null and alternative hypotheses for an experiment with one population proportion

## Question

An airline company claims in a recent advertisement that at least 94% of passenger luggage that it lost is recovered and reunited with the customer within 1 day. Hunter is a graduate student studying statistics. For a research project, Hunter wants to find out whether there is convincing evidence in support of the airline company’s claim. He randomly selects 315 passengers of the airline whose luggage was lost by the airline and found that 276 of those passengers were reunited with their luggage within 1 day. Are all of the conditions for this hypothesis test met, and if so, what are the null and alternative hypotheses for this hypothesis test?

Identify the null and alternative hypotheses for an experiment with one population proportion

## Question

The owners of a supermarket chain are looking into the effectiveness of the supermarket’s loyalty card program. Specifically, they would like to know if the percentage of shoppers in their stores who use the loyalty card has changed from 63% in 2014. Chloe works in the marketing department of the chain and is assigned to answer the owners’ inquiry. She randomly selects 196 customers from various stores in the chain and finds that 114 use the loyalty card. What are the null and alternative hypotheses for this hypothesis test?