Hypothesis Test for a Proportion with StatCrunch and MyMathlab All Steps Shown | Summary and Q&A

TL;DR

Testing the claim that the probability of home team wins is greater than 1/2 using a significance level of 0.10.

Key Insights

• 🏆 The hypothesis test analyzes the probability of the home team winning in football games.
• 😫 The sample size of 52 games provides a sizable data set for the analysis.
• 🏆 The test results indicate that the probability of home team wins is greater than 1/2.
• 🏆 A significance level of 0.10 was used to determine the test decision.
• ❓ Rejecting the null hypothesis suggests that the alternative hypothesis is true.
• 🏆 The test statistic obtained was 1.38675.
• 😀 The p-value calculated was 0.083, providing evidence to support the alternative hypothesis.

Transcript

consider a sample of 52 football games where 31 of them were won by the home team use a point 100 significance level to test the claim that the probability that the home team wins is greater than 1/2 so this is a hypothesis test for a proportion so we're given n which is the total number of observations looks like that's going to be 52 and then X i... Read More

Questions & Answers

Q: What is the significance level used in the hypothesis test?

The significance level used in the test is 0.10, which means there is a 10% chance of rejecting the null hypothesis incorrectly.

Q: How many football games were included in the sample?

The sample consisted of 52 football games.

Q: How many games were won by the home team?

Out of the 52 games, 31 were won by the home team.

Q: What is the test statistic obtained in the analysis?

The test statistic obtained is 1.38675.

Q: What does it mean to reject the null hypothesis?

Rejecting the null hypothesis means that there is sufficient evidence to support the alternative hypothesis, which states that the probability of home team wins is greater than 1/2.

Q: What is the p-value calculated in the test?

The p-value calculated in the test is 0.083.

Q: Is there enough evidence to claim that the home team wins more than half the games?

Yes, the test provides enough evidence to claim that the probability of the home team winning is greater than 1/2.

Q: What is the interpretation of the test results?

At a significance level of 0.10, there is sufficient evidence to support the claim that the probability of the home team winning is greater than 1/2.

Summary & Key Takeaways

• A sample of 52 football games was analyzed, where 31 of them were won by the home team.

• The hypothesis test for a proportion was conducted to determine if the probability of home team wins is greater than 1/2.

• The test resulted in rejecting the null hypothesis, providing sufficient evidence to claim that the probability of home team wins is greater than 1/2.