Download Probability and Statistics Chapter 8: Hypothesis Testing Answers to

Probability and Statistics
Chapter 8: Hypothesis Testing
Answers to Even Problems
8-2 Basics of Hypothesis Testing
2. Estimates and hypothesis tests are both methods of inferential statistics, but they have different
objectives. We could use the sample weights to construct a confidence interval estimate of the mean
weights of M&Ms, but hypothesis testing is used to test some claim made about the mean weight of
M&Ms.
4. The P-value of 0.001 is preferred because it corresponds to the sample evidence that most strongly
supports the alternative hypothesis that the XSORT method is effective.
6. a. 𝑝 > 0.5 b. 𝐻0 : 𝑝 = 0.5 and 𝐻1 : 𝑃 > 0.5
8. a. 𝜎 ≥ 50 b. 𝐻0 : 𝜎 = 50 and 𝐻1 : 𝜎 < 50
10. There is sufficient evidence to support the claim that when parents use the XSORT method of
gender selection, the proportion of baby girls is greater than 0.5.
12. There is sufficient evidence to reject the claim that pulse rates of adult females have a standard
deviation of at least 50.
14. 𝑧 = −1.27,
16. 𝑡 = −2.358
18. P-value = 0.0228, critical value: 𝑧 = −1.645
20. P-value = 0.1336, critical values: 𝑧 = −1.96, 𝑧 = 1.96
22. P-value = 0.0124, critical values: 𝑧 = −1.96, 𝑧 = 1.96
24. P-value = 0.0020, critical value: 𝑧 = 1.645
26. a. Fail to reject 𝐻0 b. There is not sufficient evidence to support the claim that fewer than 20%
of M&M candies are green
28. a. Reject 𝐻0 b. There is sufficient evidence to warrant rejection of the claim that women have
heights with a standard deviation equal to 5.00 cm.
8-3 Testing a Claim About a Proportion
411
2. 𝑝̂ = 1003 or 0.410. The symbol 𝑝̂ is used to represent a sample proportion.
4. a. The symbol 𝑝 represents the population proportion, but the P-value is a probability of getting
sample results that are at least as extreme as those obtained (assuming the null hypothesis is true).
b. If the P-value is very low (such as less than or equal to 0.05), “the null must go” means that we
should reject the null hypothesis. c. The statement that “if P is high, the null will fly” suggests that
with a high P-value, the null hypothesis has been provide or is supported, but we should never make
such a conclusion.
8-4 Testing a Claim About a Mean
2. df denotes the number of degrees of freedom. For the sample of 12 times, df = 11.
4. Use a 90% confidence level. The given confidence interval does contain the value of 90 seconds,
so it is possible that the value of 𝜇 is equal to 90 seconds or some lower value, so there is not sufficient
evidence to support the claim that the mean is greater than 90 seconds.
8-5 Testing a Claim About a Standard Deviation or Variance
2. a. The normality requirement for a hypothesis test of a claim about a standard deviation is much
more strict, meaning that the distribution of the population must be much closer to a normal
distribution. b. With only 10 sample values, a histogram doesn’t really give us a good picture of the
distribution, so a normal quantile plot would be better. Also, we should determine that there are no
outliers.
4. a. 𝐻0 : 𝜎 = 1.8 min and 𝐻1 : 𝜎 < 1.8 min b. 𝜒 2 = 0.694 c. Reject the null hypothesis. d. There is
sufficient evidence to support the claim that the standard deviation of waiting times of all customers is
less than 1.8 minutes. e. The change to a single waiting line is effective because the variation among
waiting times is less than it was with multiple lines.