Chapter 10
Statistical Inference About Means and Proportions
with Two Populations

Case Problem: Par, Inc.

This case can provide discussion and differing opinions as to what hypothesis test should be conducted. Students should begin to see that logical arguments exist for structuring the hypotheses differently. In some interpretations of the problem, a two - tailed test can be appropriate for Par, Inc. In other interpretations of the same problem, a one - tailed test may be preferred. We suggest accepting different formulations of the Par, Inc. hypothesis test provided convincing rationale is provided.

Letting
1 = the population mean driving distance for the current golf ball
2 = the population mean driving distance for the new golf ball,

we suggest the following hypothesis test:

H0: 1 - 2 0

Ha: 1 - 2 > 0

This formulation is based on the information that the new golf ball is being designed to “resist cuts and yet still offer good driving distances.” The research hypothesis is not to prove the new golf ball out distances the current golf ball. In fact, Par could claim an improved quality with the cut resistance improvement provided the new golf ball has the same or better driving distance. The hypotheses have been structured so that rejection of H0 corresponds to the conclusion that the new golf ball has the lower mean driving distances; this conclusion indicates that the cut resistance advantage may be offset by the loss of distance.

...1. Think about a real world: Diagnosis Congestive heart failure (CHF), non compliance with daily weight or diet/situation.
Address using an independent or related samples t test.
2. Identify the independent (grouping) and dependant (response) variables important to study
3. Explain whether an independent sample or related sample t test is appropriate and why
4. Generate a hypothesis, including null and alternative hypothesis
5. Describe what information the effect size will...

...find interval estimates for two population parameters, a population mean and a population proportion. Explain the meaning of an interval estimate of a population parameter.
An interval estimate for a specified population parameter (such as a mean or proportion) is a range of values in which the parameter is estimated to lie. In Chapter 6, you were assigned to find interval estimates for a population mean and a...

...Chapter 10
StatisticalInferences Based on Two Samples
True/False
1. An independent sample experiment is an experiment in which there is no relationship between the measurements in the different samples.
Answer: True Difficulty: Medium
2. When testing the difference between two proportions selected from populations with large independent samples, the Z test statistic is used.
Answer: True Difficulty: Medium
3. In forming a large...

...
(iii) Find the mean, median, range and standard deviation for the 1990 returns.
Annual Returns % (1990)
Mean 12.91865979
Median 11.38
Standard Deviation 9.297513067
Range 75.01
(iv) Repeat part (iii) for the 1998 returns.
Annual Returns % (1998)
Mean 6.355463918
Median 5.4
Standard Deviation 5.170830853
Range 42.76
(v) Which was the better year for investors?
• 1990 was the better year for investors in regards to annual returns...

...
1. A statistics professor has just given a final examination in his statisticalinference course. He is particularly interested in learning how his class of 40 students performed on this exam. The scores are shown below.
77 81 74 77 79 73 80 85 86 73
83 84 81 73 75 91 76 77 95 76
90 85 92 84 ...

...either sketch or write out.
Step 4
Conclusion
Mean of difference scores
T-statistic takes the same basic form (statistic minus expected value/SD)
Reported as t(9) = .85, n.s.
Statistical decision (don’t reject null all hypothesis are plausible; reject accept all alternative hypotheses)
Interpretation
Independent group t-tests
The logic of testing hypothesis about the means of two independent groups is the same as for...

...Inferences Concerning Two Means
If researchers want to compare two samples in terms of the mean scores using inferential statistics, they can utilize a confidence interval approach to the data or an approach that involves setting up and testing a null hypothesis. Whether two samples are considered to be independent or correlated is tied to the issue of the nature of the groups before data are collected on the study’s dependent variable. If the two...

...sample
The t-test is a hypothesis test. There are seven steps for a hypothesis test.
1.
2.
3.
4.
5.
6.
7.
State the null hypothesis
State the alternative hypothesis
State the level of significance
State the test statistic
Calculate
Statistical Conclusion
Experimental Conclusion
Example One-Sample t-test
The age of the head of household residents of Phoenix, Arizona has increased in the
recent years. Ten years ago the average age of head of household in...

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