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Chapter 8: Q2 (page 371)

Estimates and Hypothesis Tests Data Set 3 “Body Temperatures” in Appendix B includes sample body temperatures. We could use methods of Chapter 7 for making an estimate, or we could use those values to test the common belief that the mean body temperature is 98.6°F. What is the difference between estimating and hypothesis testing?

Short Answer

Expert verified

The difference between interval estimation and hypothesis test is that the former involves estimating the value of the population mean body temperature in the form of an interval while the latter deals with testing the difference between the sample body temperature and the value of 98.6 degrees Fahrenheit.

Step by step solution

01

Given information

It is given that the value of the mean body temperature is equal to 98.6 degrees Fahrenheit.

02

Interval estimate vs. Hypothesis test

An interval estimate, obtained using the sample values, gives a range of values within which the population parameter is likely to fall.

On the other hand, hypothesis testing is used to test if the estimated value of the population parameter from the sample has a value that is different from a given (or claimed) value.

Here, based on a set of sample values, it is needed to test whether the mean body temperature is equal to 98.6 degrees of Fahrenheit.

Thus, testing the difference between the sample mean body temperature and the hypothesized value of 98.6 degrees Fahrenheit will require the use of hypothesis testing and not interval estimation.

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Most popular questions from this chapter

PowerFor a hypothesis test with a specified significance level , the probability of a type I error is, whereas the probability of a type II error depends on the particular value ofpthat is used as an alternative to the null hypothesis.

a.Using an alternative hypothesis ofp< 0.4, using a sample size ofn= 50, and assumingthat the true value ofpis 0.25, find the power of the test. See Exercise 34 “Calculating Power”in Section 8-1. [Hint:Use the valuesp= 0.25 andpq/n= (0.25)(0.75)/50.]

b.Find the value of , the probability of making a type II error.

c.Given the conditions cited in part (a), find the power of the test. What does the power tell us about the effectiveness of the test?

In Exercises 9–12, refer to the exercise identified. Make subjective estimates to decide whether results are significantly low or significantly high, then state a conclusion about the original claim. For example, if the claim is that a coin favours heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favours heads (because it is easy to get 11 heads in 20 flips by chance with a fair coin).

Exercise 8 “Pulse Rates”

Testing Claims About Proportions. In Exercises 9–32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.

Touch Therapy Repeat the preceding exercise using a 0.01 significance level. Does the conclusion change?

Testing Hypotheses. In Exercises 13–24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim.

Earthquake Depths Data Set 21 “Earthquakes” in Appendix B lists earthquake depths, and the summary statistics are n = 600, x = 5.82 km, s = 4.93 km. Use a 0.01 significance level to test the claim of a seismologist that these earthquakes are from a population with a mean equal to 5.00 km.

Identifying H0and H1. In Exercises 5–8, do the following:

a. Express the original claim in symbolic form.

b. Identify the null and alternative hypotheses.

Pulse Rates Claim: The mean pulse rate (in beats per minute, or bpm) of adult males is equal to 69 bpm. For the random sample of 153 adult males in Data Set 1 “Body Data” in Appendix B, the mean pulse rate is 69.6 bpm and the standard deviation is 11.3 bpm.
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