The average gasoline price of one of the major oil companies in Oman has been OMR 0.95 per gallon. The company is not interested in increasing or decreasing the current prices of gasoline. A random sample of 36 of their gas stations is selected and the average price is determined to be OMR 0.945 per gallon. Furthermore, assume that the population standard deviation is OMR O.024. Then at 5% significance level the null hypothesis that the average gasoline price of OMR O.95 is rejected. Select one: O True O False
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- Suppose the mean height of women age 20 years or older in a certain country is 62.2 inches. One hundred randomly selected women in a certain city had a mean height of 61.7 inches. At the 1% significance level, do the data provide sufficient evidence to conclude that the mean height of women in the city differs from the national mean? Assume that the population standard deviation of the heights of women in the city is 3.9 inches. Set up the hypotheses for the one-mean z-test. H0: μ (≠, >, <, =) ________ppmHa: μ (≠, >, <, =) _________ppm Compute the value of the test statistic.z=__________(Round to two decimal places as needed.) Determine the critical value(s). Select the correct choice below and fill in the answer box within your choice. (Round to two decimal places as needed.) A. The critical value is zα=____________ B. The critical values are ±zα/2=±____________ C. The critical value is −zα=___________A certain breed of rat shows a mean weight gain of 65g during the first 3 months of life. A random sample of 34 rats of this breed are fed a new diet from birth until age 3 months. These 34 rats have a mean weight gain of 60.75g and a standard deviation of 3.84g. We are interested in testing whether there is reason to believe, at the 0.05 significance level, that the new diet is causing a change in the average amount of weight gained in this breed of rats. By comparing the test statistic and the critical value, what conclusion can we draw at the 0.05 significance level? Since the test statistic is more extreme than the critical value, we reject the null hypothesis. We have statistically significant evidence to conclude that average weight gain during the first 3 months of a certain breed of rat's life on the new diet is not equal to 65g. Since the test statistic is NOT more extreme than the critical value, we fail to reject the null hypothesis. We do not have statistically significant…A comparison is made between two bus lines to determine if arrival times of their regular buses from Denver to Durango are off schedule by the same amount of time. For 51 randomly selected runs, bus line A was observed to be off schedule an average time of 53 minutes, with standard deviation 15 minutes. For 60 randomly selected runs, bus line B was observed to be off schedule an average of 60 minutes, with standard deviation 11 minutes. Do the data indicate a significant difference in average off-schedule times? Use a 5% level of significance. What are we testing in this problem? difference of proportionsdifference of means single meanpaired differencesingle proportion (a) What is the level of significance?State the null and alternate hypotheses. H0: ?1 = ?2; H1: ?1 < ?2H0: ?1 = ?2; H1: ?1 ≠ ?2 H0: ?1 > ?2; H1: ?1 = ?2H0: ?1 = ?2; H1: ?1 > ?2 (b) What sampling distribution will you use? What assumptions are you making? The Student's t. We assume that both population…
- For a certain knee surgery, a mean recovery time of 13 weeks is typical. With a new style of physical therapy, a researcher claims that the mean recovery time, μ, is less than 13 weeks. In a random sample of 32 knee surgery patients who practiced this new physical therapy, the mean recovery time is 12.8 weeks. Assume that the population standard deviation of recovery times is known to be 1.1 weeks. Is there enough evidence to support the claim that the mean recovery time of patients who practice the new style of physical therapy is less than 13 weeks? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis Ho and the alternative hypothesis H₁. H Ho: O H₁:0 OO 020 ローロ OO ? (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 x-μ √n • The p-value is the area under the curve to the left of the value of the test statistic. Standard Normal Distribution 04 Step 1:…A leasing firm claims that the mean number of miles driven annually, u, in its leased cars is less than 13,180 miles. A random sample of 19 cars leased from this firm had a mean of 12,957 annual miles driven. It is known that the population standard deviation of the number of miles driven in cars from this firm is 2080 miles. Assume that the population is normally distributed. Is there support for the firm's claim at the 0.05 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. Ho H :0 (b) Determine the type of test statistic to use. O=D (Choose one) ▼ OA leasing firm claims that the mean number of miles driven annually, u, in its leased cars is less than 13,100 miles. A random sample of 50 cars leased from this firm had a mean of 13,003 annual miles driven. It is known that the population standard deviation of the number of miles driven in cars from this firm is 1120 miles. Is there support for the firm's claim at the 0.05 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. Ho :0 S H : (b) Determine the type of test statistic to use. (Choose one) D=0 (c) Find the value of the test statistic. (Round to three or more decimal places.) O#0 OO (d) Find the p-value. (Round to three or more decimal places.) (e) Can we support the leasing firm's claim that the mean number of miles driven…A leasing firm claims that the mean number of miles driven annually, µ, in its leased cars is less than 12,300 miles. A random sample of 80 cars leased from this firm had a mean of 12,150 annual miles driven. It is known that the population standard deviation of the number of miles driven in cars from this firm is 3160 miles. Is there support for the firm's claim at the 0.05 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) |(a) State the null hypothesis H, and the alternative hypothesis H . H, :0 H, :0 |(b) Determine the type of test statistic to use. (Choose one) O=0 OSO (c) Find the value of the test statistic. (Round to three or more decimal places.) OA leasing firm claims that the mean number of miles driven annually, µ, in its leased cans is less than 12460 miles. A random sample of 27 cars leased from this firm had a mean of 11839 annual miles driven. It is known that the population standard deviation of the number of miles driven in cars from this firm is 1620 miles. Assume that the population is normally distributed. Is there support for the firm’s claim at the 0.05 level of significance? The null hypothesis: H0 : _____ The alternative hypothesis: H1: ______ The type of test statistic: (choose one) _______ The value of the test statistic: ______ (round to at least three decimal places.) The p-value: _____ (round to at least three decimal places.) Can we support the leasing firm’s claim that the mean number of miles driven annually is less than 12460 miles? Yes _____, NO ______The average undergraduate cost for tuition, fees, and room and board for two-year institutions last year was $14,124. The following year, a random sample of 20 two-year institutions had a mean of $17,124 and a standard deviation of $3700. Is there sufficient evidence at the alpha level of 0.05 to conclude that the mean cost has increased. Show 6 steps of hypothesisAccording to the norms established for a history test, Grade 8 students should have an average of 81.7 with standard deviation of 8.5. If 100 randomly selected grade 8 students from a certain school district average 79.6 in this test, can we conclude that at 0.05 level of significance that Grade 8 students from this school district can be expected to have a different average than the norm of 81.7?Managers at an automobile manufacturing plant would like to examine the mean completion time, μ, of an assembly line operation. The past data indicate that the mean completion time is 44 minutes, but the managers have good reason to believe that this value has changed. The managers plan to perform a statistical test. After choosing a random sample of assembly line completion times, the managers compute the sample mean completion time to be 40 minutes. The standard deviation of the population of completion times can be assumed not to have changed from the previously reported value of 3 minutes. Based on this information, complete the parts below. (a) What are the null hypothesis H and the alternative hypothesis H₁ that should be used for the test? Ho H₁ : 0 (b) Suppose that the managers decide not to reject the null hypothesis. What sort of error might they be making? (Choose one) (c) Suppose the true mean completion time for the assembly line operation is 38 minutes. Fill in the blanks…A major car manufacturer wants to test a new catalytic converter to determine whether it meets new air population standards. The mean emission of all converter of this type must be less than 20 parts per million of carbon. 10 converters are manufactured for testing purpose and their emission levels are measured with a mean of 17.17 and a standard deviation of 2.98. 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