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Hypothesis testing for two proportions

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Wize University Statistics Textbook > Inference for Two Population Proportions

Hypothesis Testing for Two Proportions

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Harold has a life-threatening disease, Bonaria, which requires treatment. He has to consider between the two: Treatment A and Treatment B. His doctor gives him pamphlets for both options:
  • Treatment A was used to treat Bonaria since 1908. Out of random sample of 11,350 patients diagnosed with Bonaria, 7,522 were treated with success.

  • Treatment B is a relatively new and controversial treatment for Bonaria. In a sample of 3,000 patients, 1500 were treated with success.

Harold wishes to know if Treatment A has a higher success rate than treatment B by more than 14%. The appropriate hypotheses are
More Hypothesis Testing for Two Proportions Questions:
Hypothesis Testing: Two-Tailed 2 Proportions
An economist believes that a higher proportion of houses in Vancouver are overpriced compared to Toronto. He believes that a house is overpriced if it's market value has increased by more than 40% over the last 3 years. A sample of homes in both cities and whether or not they have increased in market value by more than 40% are listed below.
At the 5% level of significance, is there evidence to support the economist's opinion? State the test statistic and p-value
Hypothesis Testing: Two-Tailed 2 Proportions
An economist believes that a higher proportion of houses in Vancouver are overpriced compared to Toronto. He believes that a house is overpriced if it's market value has increased by more than 40% over the last 3 years. A sample of homes in both cities and whether or not they have increased in market value by more than 40% are listed below.
At the 5% level of significance, is there evidence to support the economist's opinion? State the test statistic and p-value
Hypothesis testing for two proportions
Black cats are considered bad luck in Canada but good luck in Japan. A random sample of households with cats was drawn in both countries to see if their owners have at least one black cat. We wish to test if Japan has a different proportion of pet owners with black cats than Canada. It turns out that the 95% confidence interval for the difference in proportions contains “0”.
(a) What is your conclusion at the 5% level of significance?
(b) Will your conclusion change if we perform a 99% confidence interval instead?
Hypothesis Testing: Two Proportions
You wish to see if shoppers at Malmart shop at the mall less often than those at Shoeless Shoes. In a sample of 90 shoppers at Malmart, 30 say they come to the mall every week. In a sample of 70 Sholess Shoes shoppers, 33 say they come to the mall every week.
What is the value test-statistic in this problem?
Hypothesis testing for two proportions
You wish to see if shoppers at Malmart shop at the mall less often than those at Shoeless Shoes. In a sample of 90 shoppers at Malmart, 30 say they come to the mall every week. In a sample of 70 Sholess Shoes shoppers, 33 say they come to the mall every week.
The appropriate null and alternative hypotheses are:
Hypothesis Testing for Two Proportions
Harold has a life-threatening disease, Bonaria, which requires treatment. He has to consider between the two: Treatment A and Treatment B. His doctor gives him pamphlets for both options:
Treatment A was used to treat Bonaria since 1908. Out of random sample of 11,350 patients diagnosed with Bonaria, 7,522 were treated with success.
Treatment B is a relatively new and controversial treatment for Bonaria. In a sample of 3,000 patients, 1500 were treated with success.
Hypothesis testing for two proportions
Black cats are considered bad luck in Canada but good luck in Japan. A random sample of households with cats was drawn in both countries to see if their owners have at least one black cat. We wish to test if Japan has a greater proportion of pet owners with cats than Canada. It turns out that the 95% confidence interval for the difference in proportions contains “0”.
(a) What is your conclusion at the 5% level of significance?
(b) Will your conclusion change if we perform a 99% confidence interval instead?
Hypothesis testing for two proportions
We want to see if the proportion of male who know how to swim differ than those of females. Suppose that your p-value is 0.006. At the 1% level of significance, your conclusion would be
Hypothesis Testing for Two Proportions
We want to see if the proportion of male who know how to swim differ than those of females. Here is a contingency table:
Which of the following are the appropriate Ho and Ha?
Hypothesis Testing for Two Proportions
Is there evidence, at the 5% significance level, that divorce rate is higher in Town A than Town B? Use a test-statistic of 1.09
Hypothesis Testing: Two-Tailed 2 Proportions
An economist believes that a higher proportion of houses in Vancouver are overpriced compared to Toronto. He believes that a house is overpriced if it's market value has increased by more than 40% over the last 3 years. A sample of homes in both cities and whether or not they have increased in market value by more than 40% are listed below.
At the 5% level of significance, is there evidence to support the economist's opinion? State the test statistic and p-value
Hypothesis testing for two proportions
Is there evidence, at the 5% significance level, that divorce rate is higher in Town A than Town B? Use a test-statistic of 1.089.
Hypothesis testing for two proportions
We want to see if the proportion of male who know how to swim differ than those of females. Suppose that your test statistic is -0.6299. At the 1% level of significance, your conclusion would be
Hypothesis Testing for two Proportions
We want to see if the proportion of male who know how to swim differs from the proportion of females. Here is a contingency table:
Which of the following are the appropriate H0 and H1?
Using a Confidence Interval for Hypothesis Tests
You wish to test Ho:p1−p2=0.30   Ha:  p1−p2≠0.30H_o:p_1-p_2=0.30\ \ \ H_a:\ \ p_1-p_2\ne0.30
You are told a 95% confidence interval for the difference in the two proportions is (−0.12, 0.03)\left(-0.12,\ 0.03\right). Should you reject the null hypothesis at each the following levels of significance?
(i) 5% level