How can you reach a hypothesis-testing conclusion by examining a confidence interval for a two independent...

How can you reach a hypothesis-testing conclusion by examining a confidence interval for a two independent sample t-test? Is it possible? If so, how?

Solutions

Expert Solution

Yes, it is possible to reach a hypothesis-testing conclusion by examining a confidence interval for a two independent sample t-test.

Suppose we are interested to test if there is any significant difference in the means of two independent samples and our test statistic is the difference of sample means.

Let the significance level of the test is , 0<<1

and (1-)100% confidence interval is (t₁, t₂). That means if we take the sample 100 times and test the difference in means, (1-)100 times this interval will be able to contain the difference between two population means and 100 times this interval is expected to fail to contain the true difference in means.

Our Null hypothesis: true difference is 0 and alternative hypothesis: true difference is not 0.

If our test statistic value falls outside the confidence interval, then we will reject the null hypothesis at 100% level of significance. If it falls inside the confidence interval then we fail to reject null hyothesis at 100% level of significance.

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Evaluate and provide example of how hypothesis testing and confidence interval are used together in healthcare...

Evaluate and provide example of how hypothesis testing and confidence interval are used together in healthcare research. Also provide a workplace example that illustrates your ideas.

The following are a few problems on hypothesis testing. The corresponding confidence interval (CI) question is...

The following are a few problems on hypothesis testing. The corresponding confidence interval (CI) question is also asked. This is a good practice for students to see how hypothesis testing results reflect in the confidence interval estimates. In the first problem, the steps are given to get the hypothesis testing results and the CI estimates. It is a good practice to follow the steps. Try to use the same steps in the subsequent problems. 1. The life span of 100...

The following are a few problems on hypothesis testing. The corresponding confidence interval (CI) question is...

Project for Chapters 8 & 9 Confidence Interval & Hypothesis Testing for a Single Population Dominick...

Project for Chapters 8 & 9 Confidence Interval & Hypothesis Testing for a Single Population Dominick Aldo owns and operates Carolina’s which is an Italian restaurant in New York. The file Single Population.xlsx is shown below and contains the amount of time that 90 tables were seated. Develop a 90% confidence interval for this random sample and interpret the results. Test the hypothesis that the average table time exceeds 98 minutes using α=.05. What is the p-value? Interpret the results....

Using either hypothesis testing or confidence interval method solve: The average size of a farm green...

Using either hypothesis testing or confidence interval method solve: The average size of a farm green county is 199 acres, and the average size of a farm in yellow county is 191. Assume the data were obtained from two samples with standard deviations of 12 acres and 38, respectively, and the sample sizes are 10 farms from Green county and 8 farms from in Yellow County. Can it be concluded at alpha= 0.05 that the average size of the farms...

Confidence Interval & Hypothesis Testing for a Single Population Dominick Aldo owns and operates Carolina’s which...

Confidence Interval & Hypothesis Testing for a Single Population Dominick Aldo owns and operates Carolina’s which is an Italian restaurant in New York. The file Single Population.xlsx is shown below and contains the amount of time that 90 tables were seated. Develop a 90% confidence interval for this random sample and interpret the results. Test the hypothesis that the average table time exceeds 98 minutes using α=.05. What is the p-value? Interpret the results. Be sure that your project shows...

Confidence Intervals and Hypothesis Testing a) Consider collecting a sample of 16 random independent values from...

Confidence Intervals and Hypothesis Testing a) Consider collecting a sample of 16 random independent values from a population with Gaussian distribution whose mean is 20 and variance is 9. Determine the 90-percent confidence interval for the sample mean. b) Repeat part (a) with the assumption that the population variance is unknown; but assume that you have determined that the unbiased estimate of the variance is 9 for your sample. c) Assume that the mean and variance of the population are...

Find a 95% confidence interval for the difference of two means when you have independent samples,...

Find a 95% confidence interval for the difference of two means when you have independent samples, both of size 36, from two populations, in which the variances are not known to be equal. In this case, n1=36, s12=8.2, the first sample mean is equal to 7.9; n2 =36, s22=10.4, the second sample mean is equal to 9.1 Interpret the interval once you find it. Namely, can you conclude one mean is greater than the other mean and if so, which...

STATCRUNCH STEPS FOR CONFIDENCE INTERVAL AND HYPOTHESIS TESTING CALCULATIONS (WEEKS 4 AND 5) Several years ago,...

STATCRUNCH STEPS FOR CONFIDENCE INTERVAL AND HYPOTHESIS TESTING CALCULATIONS (WEEKS 4 AND 5) Several years ago, a government agency reported the default rate (the proportion of borrowers who default on their loans) on a certain type of loan at 0.045 Set up the null and alternative hypotheses to determine if the default rate this year is greater than 0.045.

In this project you will be asked to find confidence interval and perform a hypothesis test...

In this project you will be asked to find confidence interval and perform a hypothesis test for the mean of one population. Be sure to show all your work neatly. Instructions The table provided below contains pulse rates after running for 1 minute, collected from females who drink alcohol ("Pulse rates before," 2013). The mean pulse rate after running for 1 minute of females who do not drink is 97 beats per minute. Do the data show that the mean...

Subjects