A consumer products company is formulating a new shampoo and is interested in foam height (in millimeters). Foam height is approximately normally distributed and has a standard deviation of 20 millimeters. The company wishes to test Ho: µ = 175 millimeters versus Hj: µ ± 175 millimeters, using the results of n= 10 samples. |What is the type I error probability if the acceptance region is 1555 iS 195 ? a. P (155
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- a) A machine is set to produce disc plates with a mean diameter of 14 mm. A sample of 8 discs gave a mean diameter, x 14.9 mm and a standard deviation, s = 1.33 mm. A test was carried out at the 5% level of significance to determine whether the machine is in good working order. Assume that the diameter of the disc follows a normal distribution. State, with reasons, whether a t-test or a z-test will be appropriate. (Determine the rejection region(s) of the test. Calculate the value of the test statistic. State, with reason, a valid conclusion for the tesi.The mean SAT score in mathematics is 528. The standard deviation of these scores is 44. A special preparation course claims that the mean SAT score, µ, of its graduates is greater than 528. An independent researcher tests this by taking a random sample of 17 students who completed the course; the mean SAT score in mathematics for the sample was 557. Assume that the population is normally distributed. At the 0.01 level of significance, can we conclude that the population mean SAT score for graduates of the course is greater than 528? Assume that the population standard deviation of the scores of course graduates is also 44. 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. D=0 OSO |(Choose one) Osample of 25 one-vear-old girls had a mean weight of 24.1 pounds with a standard deviation of 4.3 pounds. Assume that the population of weights normally d'ebuted. A pediatrician daims that the standard deviation of the weights of one-year-old girls is greater than S pounds. Do the data provide convincing evidence that the pediatrician's claim is true? Use the a = 0.01 level of significance A.) Compute the test static and explain how B.) reject or keep C.) state conclusionThe cooling system in a nuclear submarine consists of an assembly of welded pipes through which a coolant is circulated. Specifications require that weld strength must exceed 150 psi. A random sample of 20 welds resulted in a sample mean of 153.7 psi and a sample standard deviation of 11.3 psi. Which side(s) is (are) the critical region(s) located? O left side Oright side O both left and right sides O neither left nor right since there is no critical regionA car company says that the mean gas mileage for its luxury sedan is 21 mpg. You believe the mean gas mileage is lower than this and find that a random sample of 5 cars has a mean gas mileage of 19 mpg and a sample standard deviation of 4 mpg. Assume the gas mileage of all of the company's luxury sedans is normally distributed. At x = 0.10, use a t-test to assert the validity of the company's claim. 22 Should you accept the manufacturer's claim? Yes. No.A population of values has an unknown distribution with u = 165.2 and o = random sample of size n = 79. 42.2. You intend to draw a What is the mean of the distribution of sample means? (Please enter an exact answer.) What is the standard deviation of the distribution of sample means? (Please report your answer accurate to 2 decimal places.)A car company says that the mean gas mileage for its luxury sedan is 21 mpg. You believe the mean gas mileage is lower than this and find that a random sample of 5 cars has a mean gas mileage of 19 mpg and a sample standard deviation of 4 mpg. Assume the gas mileage of all of the company's luxury sedans is normally distributed. At x = 0.10, use a t-test to assert the validity of the company's claim. The null hypothesis is: Ho: μ 21 Ho: μ = 21 Ho: μ # 21An investigation of the ability of a hybrid tomato plant to produce a certain protein found that the amount x of the protein produced in the plant had a mean of 111.5 micrograms per gram of fresh weight with a standard deviation of 8.2. Consider a random sample of n = 66 hybrid tomato plants and let x represent the sample mean amount of the protein produced. Would it be expected to observe a value of x less than 110 micrograms per gram of fresh weight? Explain. Consider an event with a probability less than 0.05 unlikely. Select the correct choice below and fill in the answer box within your choice. (Round to four decimal places as needed.) O A. It would not be expected to observe a value of x less than 110 micrograms per gram of fresh weight because the probability of such an event is which is unlikely. O B. It would not be expected to observe a value of x less than 110 micrograms per gram of fresh weight because the probability of such an event is which is not unlikely. C. It would…A company claims that the mean weight per apple they ship is 120 grams with a standard deviation of 12 grams. Data generated from a sample of 49 apples randomly selected from a shipment indicated a mean weight of 122.5 grams per apple. Is there sufficient evidence to reject the company’s claim? (useα = 0.05) A. Ho: µ = 120; Ha: µ < 120; Rejection Region: z < -1.64 B. Ho: µ = 120; Ha: µ < 120; Rejection Region: t < -1.80 C. Ho: µ = 120; Ha: µ > 120; Rejection Region: z > 1.64 D. Ho: µ = 120; Ha: µ ≠ 120; Rejection Region: z < -1.96 or z > 1.96 E. Ho: µ = 120; Ha: µ ≠ 120; Rejection Region: t < -2.20 or t > 2.20A car company says that the mean gas mileage for its luxury sedan is 21 mpg. You believe the mean gas mileage is lower than this and find that a random sample of 5 cars has a mean gas mileage of 19 mpg and a sample standard deviation of 4 mpg. Assume the gas mileage of all of the company's luxury sedans is normally distributed. At x = 0.10, use a t-test to assert the validity of the company's claim. The alternative hypothesis is: HA: μ 21 HA: H = 21 HA: μ # 21The average screen time for American children age 8 to 12 is 4.75 hours. A random sample of 20 children had a mean screen time of 5.5 hours with a standard deviation of 1.12 hours. At a = 0.05, can it be concluded that the average differs from the population average? In the space provided, show all work to make your conclusion. Be sure to include null and alternative hypotheses, critical value, test value, and your conclusion.A factory that manufactures bolts is performing a quality control experiment. Each object should have a length of no more than 11 centimeters. The factory believes that the length of the bolts exceeds this value and measures the length of 93 bolts. The sample mean bolt length was 11.06 centimeters. The population standard deviation is known to be σ=0.2 centimeters. What is the test statistic z? What is the p-value? Does sufficient evidence exist that the length of bolts is actually greater than the mean value at a significance level of α=0.05?SEE MORE QUESTIONS