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Chapter 10: Problem 35

Explain when would you use the paired-samples procedure to make confidence intervals and test hypotheses.

Short Answer

Expert verified
The paired-samples procedure is used for constructing confidence intervals and testing hypotheses when dealing with pairs of observations that are dependent on each other, such as before-and-after measurements on the same subjects or dependent samples from the same population.

Step by step solution

01

Define Paired-Samples Procedure

The paired-samples procedure is a statistical technique used when we have two sets of observations that are dependent on each other, that is, one set affects the other in some way. An example would be before-and-after measurements on the same subjects or dependent samples from the same population.
02

Define Confidence Intervals

Confidence intervals are a range of values that likely encompass the true population parameter. It's calculated from the same sample data and gives an estimated range within which the parameter is likely to fall. This is usually expressed with a confidence level, indicating the probability that the interval contains the parameter.
03

Define Hypothesis Testing

Hypothesis testing is a statistical method used to make inferences or draw conclusions about a population based on a sample. It often involves making an initial claim, collecting data, and then checking if the collected data supports the claim or not.
04

When to Use Paired-Samples Procedure

You would use the paired-samples procedure to make confidence intervals and test hypotheses when working with dependent samples. This is because this procedure allows for the accounting of the correlation between the paired samples. This correlation often results in a smaller standard error which in turn leads to narrower confidence intervals and a more powerful hypothesis test.

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Most popular questions from this chapter

In a random sample of 800 men aged 25 to 35 years, \(24 \%\) said they live with one or both parents. In another sample of 850 women of the same age group, \(18 \%\) said that they live with one or both parents. a. Construct a \(95 \%\) confidence interval for the difference between the proportions of all men and all women aged 25 to 35 years who live with one or both parents. b. Test at a \(2 \%\) significance level whether the two population proportions are different. c. Repeat the test of part b using the \(p\) -value approach.

The following information was obtained from two independent samples selected from two populations with unequal and unknown population standard deviations. $$ \begin{array}{lll} n_{1}=48 & \bar{x}_{1}=.863 & s_{1}=.176 \\ n_{2}=46 & \bar{x}_{2}=.796 & s_{2}=.068 \end{array} $$ Test at a \(1 \%\) significance level if the two population means are different.

When are the samples considered large enough for the sampling distribution of the difference between two sample proportions to be (approximately) normal?

Assuming that the two populations have unequal and unknown population standard deviations, construct a \(99 \%\) confidence interval for \(\mu_{1}-\mu_{2}\) for the following. $$ \begin{array}{lll} n_{1}=48 & \bar{x}_{1}=.863 & s_{1}=.176 \\ n_{2}=46 & \bar{x}_{2}=.796 & s_{2}=.068 \end{array} $$

A car magazine is comparing the total repair costs incurred during the first three years on two sports cars, the T-999 and the XPY. Random samples of 45 T-999s and 51 XPYs are taken. All 96 cars are 3 years old and have similar mileages. The mean of repair costs for the 45 T-999 cars is \(\$ 3300\) for the first 3 years. For the 51 XPY cars, this mean is \(\$ 3850\). Assume that the standard deviations for the two populations are \(\$ 800\) and \(\$ 1000\), respectively. a. Construct a 99\% confidence interval for the difference between the two population means. b. Using a \(1 \%\) significance level, can you conclude that such mean repair costs are different for these two types of cars? c. What would your decision be in part b if the probability of making a Type I error were zero? Explain.
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