# (Answered) MATH399N Week 7 Assignment: Developing Hypothesis and Understanding Possible Conclusions for Proportion

Question

A human resources representative claims that the proportion of employees earning more than \$50{,}000 is less than 40\%. To test this claim, a random sample of 700 employees is taken and 305 employees are determined to earn more than \$50{,}000.

The following is the setup for this hypothesis test:

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

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:

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

# 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?

# Question

Austin works in the marketing department for a large cable company. Recently, he heard that 56% of cable TV subscribers are considering dropping their cable TV subscription. He tests the claim by randomly selecting a sample of cable TV subscribers and asking whether they are considering dropping their cable TV subscription. Austin finds that 122 of the 224 he surveyed are considering dropping their cable TV subscription. What are the null and alternative hypotheses for this hypothesis test?

# Question

An airline company claims in a recent advertisement that more than 94% of passenger luggage that is 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?

Question

A researcher claims that the proportion of people who are right-handed is greater than 70%. To test this claim, a random sample of 600 people is taken and its determined that 424 people are right-handed.

The following is the setup for this hypothesis test:

{H0:p=0.70Ha:p>0.70

Find the test statistic for this hypothesis test for a proportion.

In your calculations, round the value for the sample proportion to 3 decimal places. Round your answer to 2 decimal places.

# Question

Colton makes the claim to his classmates that less than 50% of newborn babies born this year in his state are boys. To prove this claim, he selects a random sample of 344 birth records in his state from this year. Colton found that 176 of the newborns are boys. What are the null and alternative hypotheses for this hypothesis test?

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.

In your calculations, round the value for the sample proportion to 3 decimal places. Round your answer to 2 decimal places.

# Solution:

Question

A human resources representative claims that the proportion of employees earning more than \$50{,}000 is less than 40\%. To test this claim, a random sample of 700 employees is taken and 305 employees are determined to earn more than \$50{,}000.

The following is the setup for this hypothesis test:

\left\{\begin{array}{l}H_0:\;p=0.40\\H_a:\;p<0.40\end{array}\right.

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

Test Statistic=1.94

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=0.05Ha:p<0.05

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