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Comparison of two means - the t-test

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One of the most commonly used statistical techniques is the comparison of two means, also known as the t-test (for this you need quantitative, or interval level data). If you used the same data to compare means with equal sample sizes, how would the results compare if you used the paired sample, independent sample equal variance, and independent sample unequal variance? Which is the most "conservative" and why might you use it by default?

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The questions are related to Students t test, One sample t test, decision rule, confidence level, independent sample t test, paired t test, p value and test statistic.

Exercise 14
(a) State the decision rule, (b) compute the pooled estimate of the population variance, (c) compute the test statistic, (d) state your decision about the null hypothesis, and (e) estimate the p-value.

The null and alternate hypotheses are:
A random sample of 15 observations from the first population revealed a sample mean of 350 and a sample standard deviation of 12. A random sample of 17 observations from the second population revealed a sample mean of 342 and a sample standard deviation of 15. At the .10 significance level, is there a difference in the population means?

Exercise 18
Use the five-step hypothesis testing procedure for the following exercises.
The Tampa Bay (Florida) Area Chamber of Commerce wanted to know whether the mean weekly salary of nurses was larger than that of school teachers. To investigate, they collected the following information on the amounts earned last week by a sample of school teachers and nurses.
School teachers ($) 845 826 827 875 784 809 802 820 829 830 842 832
Nurses ($) 841 890 821 771 850 859 825 829
Is it reasonable to conclude that the mean weekly salary of nurses is higher? Use the .01 significance level. What is the p-value?

Exercise 22
The federal government recently granted funds for a special program designed to reduce crime in high-crime areas. A study of the results of the program in eight high-crime areas of Miami, Florida, yielded the following results.
Number of Crimes by Area
Before 14 7 4 5 17 12 8 9
After 2 7 3 6 8 13 3 5
Has there been a decrease in the number of crimes since the inauguration of the program? Use the .01 significance level. Estimate the p-value.

Exercise 26
A coffee manufacturer is interested in whether the mean daily consumption of regular-coffee drinkers is less than that of decaffeinated-coffee drinkers. A random sample of 50 regular-coffee drinkers showed a mean of 4.35 cups per day, with a standard deviation of 1.20 cups per day. A sample of 40 decaffeinated-coffee drinkers showed a mean of 5.84 cups per day, with a standard deviation of 1.36 cups per day. Use the .01 significance level. Compute the p-value.

See attached file for full problem description.

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