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Chapter 8: Q23 (page 372)

Critical Values. In Exercises 21–24, refer to the information in the given exercise and do the following.

a. Find the critical value(s).

b. Using a significance level of α= 0.05, should we reject H0or should we fail to reject H0?

Exercise 19

Short Answer

Expert verified

a. The critical values are -1.96 and 1.96.

b. The null hypothesis is rejected.

Step by step solution

01

Given information

A test statistic value of z=2.01 is obtained, and the claim to be tested is p≠0.345.

02

Hypotheses and tail of the test

In correspondence with the given claim, the following hypotheses are set up:

Null Hypothesis: p=0.345

Alternative Hypothesis: p≠0.345

Since there is a not equal sign in the alternative hypothesis, the test is two-tailed.

03

Critical value

a.

The critical values of z corresponding to the two-tailed test at α=0.05are -1.96 and 1.96.

04

Decision about the test

b.

If the test statistic value does not lie between the critical values, then the null hypothesis is rejected.

Here, the value of the test statistic (2.01) does not lie between the critical values (greater than 1.96). Thus, the null hypothesis is rejected.

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Most popular questions from this chapter

P-Values. In Exercises 17–20, do the following:

a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.

b. Find the P-value. (See Figure 8-3 on page 364.)

c. Using a significance level of α = 0.05, should we reject H0or should we fail to reject H0?

The test statistic of z = -2.50 is obtained when testing the claim that p<0.75

Type I and Type II Errors. In Exercises 29–32, provide statements that identify the type I error and the type II error that correspond to the given claim. (Although conclusions are usually expressed in verbal form, the answers here can be expressed with statements that include symbolic expressions such as p = 0.1.).

The proportion of people who write with their left hand is equal to 0.1.

In Exercises 1–4, use these results from a USA Today survey in which 510 people chose to respond to this question that was posted on the USA Today website: “Should Americans replace passwords with biometric security (fingerprints, etc)?” Among the respondents, 53% said “yes.” We want to test the claim that more than half of the population believes that passwords should be replaced with biometric security.

Null and Alternative Hypotheses Identify the null hypothesis and alternative hypothesis.

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 When she was 9 years of age, Emily Rosa did a science fair experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left hand, and then she asked the therapists to identify the selected hand by placing their hand just under Emily’s hand without seeing it and without touching it. Among 280 trials, the touch therapists were correct 123 times (based on data in “A Close Look at Therapeutic Touch,” Journal of the American Medical Association, Vol. 279, No. 13). Use a 0.10 significance level to test the claim that touch therapists use a method equivalent to random guesses. Do the results suggest that touch therapists are effective?

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).

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