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Confidence Intervals for Matched Pairs

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Wize University Statistics Textbook > Match Pairs (Dependent Means)

Hypothesis Testing for Matched Pairs

3 Activities

Wize University Statistics Textbook > Match Pairs (Dependent Means)

Confidence Intervals for Matched Pairs

2 Activities

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Mark Yourself Question
  1. Grab a piece of paper and try this problem yourself.
  2. When you're done, check the "I have answered this question" box below.
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Copeman is a private medical clinic. It has a total of 185 locations in B.C. and Ontario. In their efforts to rebrand the company to make it look more luxurious, all the locations were renovated last year. The executives randomly sampled 25 locations from each province and compared their respective sales revenues before and after renovations. Results:

Sample mean of the differences, $5,285
Sample standard deviation of the differences, $25,875
Sample size, n = 25

1. Is there evidence at the 1% level of significance that sales are different before and after renovations? ( here difference=after−beforedifference = after - before )

2. Construct a 95% confidence interval for the difference in means. What does it mean (in plain English)?
More Hypothesis Testing for Matched Pairs Questions:
Hypothesis Testing: Matched Pairs
Seven hockey players try two types of sticks. The number of goals scored using both sticks is recorded for all seven players. Here are the results:
We wish to test if the players will score on average more goals using stick A
Using a p-value of 0.0027, the appropriate conclusion at the 1% level of significance is
Hypothesis Testing: Matched Pairs
In a test, to see if the mean of one population is different than the mean of another population, the appropriate Ho and Ha are
Hypothesis Testing for Matched Pairs
You wish to test if being a member of a union increases hourly wages, in dollars, for the average construction worker. A sample of 18 construction workers' earnings were recorded prior to and after forming a union.
The results are: mean difference = −4.135-4.135 standard deviation of differences = 7.197.19
Carry out a test to see if there is a difference in hourly wages
Matched Pairs for Two Dependent Means
We wonder if judging differs when a judge give scores during the preliminary competition vs. the finale for talent shows. A random sample of 16 judges reveals the following data:
(a) At the 1% significance level, is there is a significant difference between the prices people are willing to pay based on the posters they are shown?
(b) Explain why we are not doing a two-sample test.
Hypothesis testing for Matched Pairs
A matched pairs design hypothesis test is conducted to see if having access to a practice midterm helps improve your test score. The following data is recorded:
A total of 40 students participated in the study.
1. Calculate the test-statistic?
Hypothesis testing for matched pairs
The CEO of ABC Coffee Shop wishes to know if training their employees will make them quicker at serving customers. He randomly selects 7 employees and records the number of hourly customers served without training for four days and with training for another four day period. Here are his results:
a) At the 10% level of significance, what should the CEO conclude?
Hypothesis testing for matched pairs
Copeman is a private medical clinic in B.C. and Ontario. In their efforts to rebrand the company to make it look more luxurious, all the locations were renovated last year. The executives randomly sampled 25 locations from each province and compared their respective sales revenues before and after renovations. Results:
Sample mean of the differences = $5,285
Sample standard deviation of the differences = $25,875
More Confidence Intervals for Matched Pairs Questions:
Matched Pairs for Two Dependent Means
We wonder if judging differs when a judge give scores during the preliminary competition vs. the finale for talent shows. A random sample of 16 judges reveals the following data:
(a) At the 1% significance level, is there is a significant difference between the prices people are willing to pay based on the posters they are shown?
(b) Explain why we are not doing a two-sample test.
Confidence Interval for Matched Pairs
A 90% confidence interval for the difference in the mean IQ scores between males and females is (−4,7)(-4, 7). Interpret the result.
Confidence intervals for matched pairs
The cabbage diet, invented by Dr.Dumb, aims at helping people lose weight. According to this diet, eating lots of cabbage soup can make you feel full thus reducing the need for unnecessary consumption of calories. Six people are asked to track the number of calories consumed during a regular week and a week when they were on the cabbage diet. The number of calories consumed is recorded below:
Calculate a 99% confidence interval.
Confidence intervals for matched pairs
A matched pairs design hypothesis test is conducted to see if having access to a practice midterm helps improve your test score. The following data is recorded:
A total of 40 students participated in the study.
Calculate a 95% confidence interval.