We will take a random sample of 30 vehicles of a certain make and model and measure the fuel efficiency in miles per gallon (mpg) of each of them. We will conduct a hypothesis test at the 10% level of significance to determine whether there is evidence that the true mean fuel efficiency of all cars of this make and model differs from 32 mpg. What is the probability of failing to reject Ho if the true mean is in fact 32 mpg? (A) 0.10 (B) 0.95 (C) 0.05 (D) 0.90 (E) 0.20
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- A physical therapist wanted to know whether the mean step pulse of men was less than the mean step pulse of women. She randomly selected 54 men and 70 women to participate in the study. Each subject was required to step up and down a 6-inch platform. The pulse of each subject was then recorded. The following results were obtained. Two sample T for Men vs Women N Mean StDev SE Mean Men Women 98% CI for mu Men - mu Women (- 12.20, - 1.00) T-Test mu Men = mu Women (vs H2 O C. Ho: H1 = H2; Ha: H1 #H2 (b) Identify the P-value and state the researcher's conclusion if the level of significance was a = 0.01. What is the P-value? P-value =According to previous studies, the mean distance each visitor in Greenspan National Park hikes during their visit is 30 kilometers. The park recently closed its shuttle system, which used to transport hikers to many of the park's most popular hiking trails. Because of this, an administrator at the park suspects the mean distance, µ, is now less than 30 kilometers. The administrator chooses a random sample of 45 visitors. The mean distance hiked for the sample is 29.5 kilometers. Assume the population standard deviation is 9.9 kilometers. Can the administrator conclude that the mean distance hiked by each visitor is now less than 30 kilometers? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis H, and the alternative hypothesis H,. O[ D=0 H: µ < 30 ? (b) Perform a Z-test and find the p-value. Here is some information to help you with your z-test. • The value of the test statistic is given by 1 – x • The p-value is the area under the curve to…A research study has two samples, each with n = 6, and the two experimental treatments used in each sample are being compared using an independent-measures t statistic. What is the df value for the t statistic in this study? a. df = 14 b. df = 12 c. df = 11 d. df = 10
- Water specimens are taken from water used for cooling as it is being discharged from a power plant into a river. It has been determined that as long as the mean temperature of the discharge is at most 150F, there will be no negative effects on the river's ecosystem. To investigage whether the plant is in compliance with regulations that prohibit a mean discharge water temperature above 150F, researchers will take 50 specimens at randomly selected times and record the temperature of each specimen. The resulting data will be used to test the hypotheses:H0:μ≤150FH0:μ≤150F Ha:μ>150FHa:μ>150F.(a) In the context of this problem, describe Type I and Type II errors.Type I Error:Select an answer A Type I error is not obtaining convincing evidence that the mean water temperature is greater than 150F when in fact it is greater than 150F. A Type I error is obtaining convincing evidence that the mean water temperature is greater than 150F when in fact it is at most 150F. Type II…A hypertensions trial is mounted and 12 participants are randomly assigned to receive either a new medication or a placebo. Each participant takes assigned medication and their systolic blood pressure (SBP) is recorded after 6 months on the assigned medication the data are shown in table 7-9 is there a difference in the mean SBP between treatment? Run the appropriate test at a =0.05Each person in random samples of 227 male and 293 female working adults living in a certain town in Canada was asked how long, in minutes, his or her typical daily commute was. Is there enough evidence to show that there is a difference in mean commute times for male and female working residents of this town? (Use males females) Male Female Sample size X S Sample size x S 227 30.2 24.0 293 27.9 24.3 Find the test statistic. (Round your answer to two decimal places.) Find the df. (Round your answer down to the nearest whole number.) df= Use technology to find the P-value. (Round your answer to four decimal places.) P-value= Is there enough evidence to show that there is a difference in mean commute times for male and female working residents of this town? Use a significance level of 0.05. Yes No
- Is the proportion of wildfires caused by humans in the south higher than the proportion of wildfires caused by humans in the west? 367 of the 526 randomly selected wildfires looked at in the south were caused by humans while 390 of the 594 randomly selected wildfires looked at the west were caused by humans. What can be concluded at the a = 0.01 level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Ho: Select an answer > Select an answer > Select an answer O (please enter a decimal) H j: Select an answer Select an answer > Select an answer O (Please enter a decimal) c. The test statistic (please show = your answer to 3 decimal places.) d. The p-value (Please show your answer to %3D 4 decimal places.)A physical therapist wanted to know whether the mean step pulse of men was less than the mean step pulse of women. She randomly selected 54 men and 75 women to participate in the study. Each subject was required to step up and down a 6-inch platform. The pulse of each subject was then recorded. The following results were obtained. N Mean StDev SE Mean Men Women 95% Cl for mu Men - mu Women - 9.81, - 0.79) T-Test mu Men = mu Women (vs H2 Oc. Họ: H1 = H2; Hai H1Mark performed a two-sample z-test for proportions to test the hypothesis that there was no difference in the proportion who support increasing student fees between male and female students at a particular university. Mark obtained a z-statistic of 0. Based on this information, which of the following is always true. The sample proportions for male and females will be the same as the hypothesized proportions for male and female students at this university. The sample proportions for both male and female students at this university will be 0. All male and female students in the sample will feel the same way about supporting the increase in student fees. The sample proportions will be the same for both male and female students at this university. Test whether p1>p2 The sample data are x1=116,n1=258,x2=135,n2=311. Conduct a test at the α=0.10 level of significance. Determine the correct null and alternative hypothesis below. Determine the test statistic. Find the P-value: What is…The next six questions refer to the following scenario: A random sample of 25 students were asked to self-identify as "statistics-lovers" or "statistics-adorers." 16 students self-identified as "lovers" and 9 students as "adorers." Below table summarizes the mean of a statistics test and standard deviation that was given after the self-identification. Test the following hypothesis at alpha=5% (0.05). HO: Mean Statistics Lovers = Mean Statistics Adorers HA: Mean Statistics Lovers Mean Statistics Adorers You can assume equal variance.Alpha equals 0.01 level of significance for the given sample data.Katie is interested if an association exists between age and sleep habits. She selects a random sample of 68 adults in three age groups and determines whether they sleep less than 7 hours, between 7 and 8 hours, or more than 8 hours each night. She would like to determine if there is convincing evidence of an association. Let = 0.05. What are the hypotheses for this test? H0: There is an association between age and sleep habits.Ha: There is no association between age and sleep habits. H0: There is no association between age and sleep habits.Ha: There is an association between age and sleep habits. H0: There is no difference in the distribution of age and sleep habits.Ha: There is a difference in the distribution of age and sleep habits. H0: There is a difference in the distribution of age and sleep habits.Ha: There is no difference in the distribution of age and sleep habits.