Introductory Statistics (10th Edition)
10th Edition
ISBN: 9780321989178
Author: Neil A. Weiss
Publisher: PEARSON
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Chapter 10.2, Problem 64E
a.
To determine
Illustratethe relationship between the hypothesis test and confidence interval.
b.
To determine
Illustrate the relationship between the hypothesis test and confidence interval.
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Independent random samples of sizes n1 = 204 and n2 = 204 were taken from two populations. In the first sample, 179 of the individuals met a certain criteria whereas in the second sample, 181 of the individuals met the same criteria.
Test the null hypothesis H0:p1=p2H0:p1=p2versus the alternative hypothesis HA:p1>p2HA:p1>p2.
Calculate the z test statistic, testing the null hypothesis that the population proportions are equal. Round your response to at least 2 decimal places.
What is the approximate value of the p-value? round to four decimal places.
A hypothesis test produces a t statistic of t=2.01.If the researcher is using a two tailed test with x=0.05,how large does the sample have to be in order to reject the null hypothesis?
When is a researcher at risk of making a Type II error?
Group of answer choices:
whenever H0 is rejected
whenever H1 is rejected
whenever H0 fails to be rejected
The risk of a Type II error is independent of the decision from a hypothesis test.
Chapter 10 Solutions
Introductory Statistics (10th Edition)
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- a hypothesis test produces a t statistic of t=2.3. if the researcher is using a two tailed test with a=0.05 how large does the sample have to bw in order to reject the null hypothesis?arrow_forwardA hypothesis test was conducted, at α = 0.05, to determine whether a certain chemical compound lasts longer than 30 seconds under a certain specified condition. The hypotheses used were: H0: µ = 30 Ha: µ > 30 A sample mean of 37.4 seconds was obtained from a sample of size n = 80. All statistical assumptions were met, and a p-value of p = 0.0089 was obtained. Which of the following is correct? a) If the null hypothesis were in reality true that the population mean was equal to 30, then the probability of observing a sample mean of 37.4 seconds from a sample of size n = 80 would be only .0089. b) If the null hypothesis were in reality false that the population mean was equal to 30, then the probability of observing a sample mean of 37.4 seconds (or less) from a sample of size n = 80 would be only .0089. c) If the null hypothesis were in reality true that the population mean was equal to 30, then the probability of observing a sample mean of 37.4 seconds (or greater) from…arrow_forwardA hypothesis test produces a t statistic of t = 2.30. If the researcher is using a two-tailed test with a = .05, how large does the sample have to be in order to reject the null hypothesis?arrow_forward
- 1. In hypothesis testing, the value against which a test statistic is compared to determine whether or not the null hypothesis is rejected. 2. Calculate the general t statistic if estimate is equal to 3, hypothesized value is equal to 2.5 and the standard error is equal to 0.4. 3. Calculate the general t statistic if estimate is equal to 2.3, hypothesized value is equal to 2 and the standard error is equal to 0.2. 4. Calculate the general t statistic if estimate is equal to 2.1, hypothesized value is equal to 0.75 and the standard error is equal to 0.5. 5. Calculate the general t statistic if estimate is equal to 1.6, hypothesized value is equal to 0.35 and the standard error is equal to 0.8. 6. Calculate the general t statistic if estimate is equal to 1.75, hypothesized value is equal to 1 and the standard error is equal to 0.6. 7. Calculate the general t statistic if estimate is equal to 2.5, hypothesized value is equal to 2.1 and the standard error is equal to 0.2. 8.…arrow_forward1) For a two-tailed hypothesis using a z-distribution, find the critical values (z-scores)that will give you a critical region with an alpha of the following values: a) alpha = 0.20 b) alpha = 0.10 c) alpha = 0.05 d) alpha = 0.01 e) alpha = 0.001arrow_forwardIn performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is not equal to 4.8, a random sample of 25 items is selected. The sample mean is 4.1 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The level of significance is selected to be 0.10. The critical value found in the "t" table "t" for this problem is??? a.1.711 b.2.492 c.2.797 d.3.227 e.1.318arrow_forward
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- Which of the following statements is consistent with hypothesis testing? a. If conducted correctly, hypothesis testing eliminates the risk of error. b. A low alpha level increases the size of the critical region(s). c. The edges of the distribution of sample means are consistent with the alternative hypothesis. d. All else equal, a one-tailed hypothesis test requires a more extreme treatment effect to detect statistical significance than a two-tailed hypothesis test.arrow_forwardConduct a test at the alphaαequals=0.05 level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the P-value. Assume the samples were obtained independently from a large population using simple random sampling. Test whether p1>p2. The sample data are x1=120, n1=248, x2=133, and n2=302. (a) Choose the correct null and alternative hypotheses below. A. Upper H 0 : p 1 equals p 2H0: p1=p2 versus Upper H 1 : p 1 not equals p 2H1: p1≠p2 B. Upper H 0 : p 1 equals p 2H0: p1=p2 versus Upper H 1 : p 1 less than p 2H1: p1<p2 C. Upper H 0 : p 1 equals 0H0: p1=0 versus Upper H 1 : p 1 not equals 0H1: p1≠0 D. Upper H 0 : p 1 equals p 2H0: p1=p2 versus Upper H 1 : p 1 greater than p 2H1: p1>p2 Your answer is correct. (b) Determine the test statistic. z0equals=nothing (Round to two decimal places as needed.)arrow_forward(a) What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of error of 0.2 if a preliminary estimate for p is 0.38? Recall that the minimal sample size n for a given maximal margin of error when a preliminary estimate for p is known can be found using the formula n = p(1 − p) zc E 2 , where E is the maximal margin of error.We are interested in the minimal sample size for a 95% confidence interval with a maximal margin of error of 0.2. The table below lists critical values for confidence intervals at different levels of confidence. Confidence Interval Critical Values zc Level of Confidence c Critical Value zc 0.70, or 70% 1.04 0.75, or 75% 1.15 0.80, or 80% 1.28 0.85, or 85% 1.44 0.90, or 90% 1.645 0.95, or 95% 1.96 0.98, or 98% 2.33 0.99, or 99% 2.58 According to this table, for a 95% confidence level, z0.95 = 1.96. We want the confidence interval to have a maximal margin of error of 0.2 and…arrow_forward
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