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Hypothesis Testing for Independent Means

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Wize University Statistics Textbook > Inference for Two Population Means

Hypothesis Testing for Two Independent Means

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Mr. Emin loves going to Starbucks drive-thru on his busy mornings but he can’t help feeling frustrated by the amount of time he has to wait to be served. He decides to go to Starbucks for 5 days and Tim Hortons for 7 days. He records the length of time, rounded to the nearest minute he has to wait each day to be served. Here is the data

The standard deviation for Starbucks waiting time is 3.082.
The standard deviation for Tim Hortons waiting time is 2.160.
He wishes to know if there is a difference in the mean waiting times.

a) State the appropriate Ho and Ha in words and in symbols.
b) Compute the test-statistic
c) Find the p-value and state your conclusion at the 10% level of significance.
More Hypothesis Testing for Two Independent Means Questions:
Hypothesis Testing: One-Tailed Two Independent Means
We wish to test the hypothesis that people exercising regularly sleep more on average than those that don't exercise at all. Here is data on a group of individuals for both groups. The number of hours of sleep for each person is recorded.
Let μ1\mu_1 represent the mean hours of sleep for people that exercise regularly.
Let μ2\mu_2 represent the mean hours of sleep for people that don't exercise.
Hypothesis Testing: Two Independent Means
You wish to test Ho:μA−μB=0   Ha:μA−μB≠0H_o:\mu_A-\mu_B=0\ \ \ H_a:\mu_A-\mu_B\ne0
A 95% confidence interval for the difference between the two means is (−1.64,2.75)(-1.64, 2.75)
Which of the following conclusions is valid?
Hypothesis Testing: Two Independent Means
Professor Karl has two large statistics classes. He teaches one class in the morning and one in the evening. He samples students in both classes to assess his teaching performance. He uses their latest quiz marks for his assessment.
Here is some summarized statistics:
If Professor Karl wants to test if the mean quiz marks of the two classes are different, he should use
Hypothesis Testing: Two Independent Means
Professor Donald Frump is interested in investigating whether people lose more weight, in kilograms, on a low-fat diet or high-fat diet. He randomly samples a group of people on each diet and compares the results. Which hypothesis test should he use and why?
Hypothesis Testing for Independent Means
Statistics KANATA reports that on average males earn more than females when controlling for job occupation and other factors such as level of experience. You collect a random sample of 10 males and 9 females in Canada and record the following data:
In addition, statistics KANATA reports that since 1900 the standard deviations of the earnings are roughly equal.
a) At the 5% level of significance, what is your conclusion based on the data you collected when you test the reported numbers by Stats KANATA.
Hypothesis Testing for Independent Means
Red Fish and Blue Fish are randomly sampled. Is there evidence that mercury levels are higher in Blue Fish than Red Fish? Assume unequal variances. Summary:
State the hypotheses.
Is this a one-tail or two-tail test?
Hypothesis Testing: One-Tailed Two Independent Means
We wish to test the hypothesis that people exercising regularly sleep more on average than those that don't exercise at all. Here is data on a group of individuals for both groups. The number of hours of sleep for each person is recorded.
Let μ1\mu_1 represent the mean hours of sleep for people that exercise regularly.
Let μ2\mu_2 represent the mean hours of sleep for people that don't exercise.
Hypothesis testing for two independent means
Red Fish and Blue Fish are randomly sampled. Is there evidence that mercury levels are higher in Blue Fish than Red Fish? Assume unequal variances. Summary:
It was assumed that the variances of the populations were different (even though the sample standard deviations suggest otherwise!). What is the conclusion at the 1% level of significance?
Hypothesis Testing for Two Independent Means
Statistics KANATA reports that on average males earn more than females when controlling for job occupation and other factors such as level of experience. You collect a random sample of 10 males and 9 females in Canada and record the following data:
In addition, statistics KANATA reports that since 1900 the standard deviations of the earnings are roughly equal.
a) At the 5% level of significance, what is your conclusion based on the data you collected when you test the reported numbers by Stats KANATA.
Hypothesis Testing for Two Independent Means
We wish to test the hypothesis that people exercising regularly sleep more on average than those that don't exercise at all. Here is data on a group of individuals for both groups. The number of hours of sleep for each person is recorded. Assume the population standard deviations are different.
Let μ1\mu_1 represent the mean hours of sleep for people that exercise regularly.
Let μ2\mu_2 represent the mean hours of sleep for people that don't exercise.
Hypothesis testing for two independent means
An experiment is conducted to compare the starting salaries of men and women college graduates who find jobs, we sample 10 men and 10 women and find that men earn a starting salary of $43,930 and women earn a starting salary of $43,530. The populations are normally distributed, with a standard deviation of $11,665 for men and $11,617 for women. Is there evidence that the average starting salaries differ?