A manufacturer has developed a new fishing line, which the company claims have a mean breaking strength of 15 kilograms with a standard deviation of 0.5 kilogram. To test the hypothesis that μ = 15 kilograms against the alternative that μ < 15 kilograms, a random sample of 50 lines will be tested. The critical region is defined to be x < 14.9 a. Find the probability of committing a type I error when H, is true. b. Evaluate ß for the alternatives μ = 14.8 and μ = 14.9 kilograms.

A company manufactures light bulbs. The company wants the bulbs to have a mean life span of 993 hours. This average is maintained by periodically testing random samples of 25 light bulbs. If the​ t-value falls between −t0.90 and t0.90​, then the company will be satisfied that it is manufacturing acceptable light bulbs. For a random​ sample, the mean life span of the sample is 999 hours and the standard deviation is 23 hours. Assume that life spans are approximately normally distributed. Is the company making acceptable light​ bulbs? Explain.   the company ___making acceptable light bulbs because t-value for the sample is t= and t0.90 = ( round two decimal places)

Heart rates are determined before and 30 minutes after a Kettleball workout. It can be assumed that heart rates (bpm) are normally distributed. Use the data provided below to test to determine if average heart rates prior to the workout are significantly lower than 30 minutes after a Kettleball workout at the 0.02 level of significance. Let μ₁ = mean before workout. Select the correct Hypotheses: Ho:με 2 με Η: μι = με Η: μη μ₂ O O O Conclusion: before 69 69 65 62 63 61 after 73 75 72 70 68 59 O Fail to Reject Ho ● Reject Ho Test Statistic = p-value = Ho:μd = 0 H₁: Hd ‡0 O [three decimal accuracy] [three decimal accuracy] Ho:μα 20 Ha:Pa 0 O Interpret the conclusion in context: ● There is enough evidence to suggest the mean bpm before a Kettleball workout is lower than 30 minutes after the workout. O There is not enough evidence to suggest the mean bpm before a Kettleball workout is lower than 30 minutes after the workout.

A process that manufactures glass sheets is supposed to be calibrated so that the mean thickness μ of the sheets is more than 4 mm. The standard deviation of the sheet thicknesses is known to be well approximated by σ = 0.23 mm. Thicknesses of each sheet in a sample of sheets will be measured, and a test of the hypothesis H0 : μ ≤ 4 versus H1 : μ > 4 will be performed. Assume that, in fact, the true mean thickness is 4.04 mm. Section 06.07 Exercise 06.a a) If 100 sheets are sampled, what is the power of a test made at the 5% level? The power of a test made at the 5% level is _____. b) How many sheets must be sampled so that a 5% level test has power 0.95? ______ sheets must be sampled so that a 5% level test has power 0.95.c) If 100 sheets are sampled, at what level must the test be made so that the power is 0.90? The test must be made at _____% level so that the power is 0.90. d) If 100 sheets are sampled and the rejection region is  X¯ ≥ 4.02, what is the power of the test?…

A company manufactures tennis balls. When its tennis balls are dropped onto a concrete surface from a height of 100 inches, the company wants the mean height the balls bounce upward to be 54.7 inches. This average is maintained by periodically testing random samples of 25 tennis balls. If the t-value falls between - to 99 and to 99, then the company will be satisfied that it is manufacturing acceptable tennis balls. A sample of 25 balls is randomly selected and tested. The mean bounce height of the sample is 56.7 inches and the standard deviation is 0.25 inch. Assume the bounce heights are approximately normally distributed. Is the company making acceptable tennis balls? Find -to 99 and to.99- - to.99 = to.99 = (Round to three decimal places as needed.) Find the t-value. t-value = Is the company making acceptable tennis balls? Choose the correct answer below. O A. The tennis balls are not acceptable because the t-value falls outside -tn og and to oa.

A process that manufactures glass sheets is supposed to be calibrated so that the mean thickness μ of the sheets is more than 4 mm. The standard deviation of the sheet thicknesses is known to be well approximated by σ = 0.23 mm. Thicknesses of each sheet in a sample of sheets will be measured, and a test of the hypothesis H0 : μ ≤ 4 versus H1 : μ > 4 will be performed. Assume that, in fact, the true mean thickness is 4.04 mm. Section 06.07 Exercise 06.a a) If 100 sheets are sampled, what is the power of a test made at the 5% level? The power of a test made at the 5% level is _____. b) How many sheets must be sampled so that a 5% level test has power 0.95? ______ sheets must be sampled so that a 5% level test has power 0.95.c) If 100 sheets are sampled, at what level must the test be made so that the power is 0.90? The test must be made at _____% level so that the power is 0.90. d) If 100 sheets are sampled and the rejection region is  X¯ ≥ 4.02, what is the power of the test?…

A company manufactures tennis balls. When its tennis balls are dropped onto a concrete surface from a height of 100 inches, the company wants the mean height the bails bounce upward to be 55.4 inches. This average is maintained by periodically testing random samples of 25 tennis balls. If the t-value falls between - to 90 and to so. then the company will be satisfied that it is manufacturing acceptable tennis balls. A sample of 25 balls is randomly selected and tested. The mean bounce height of the sample is 56.2 inches and the standard deviation is 0.25 inch. Assume the bounce heights are approximately normally distributed. Is the company making acceptable tennis balls? Find - to so and to so -o s0 to so O (Round to three decimal places as needed.)

A process that manufactures glass sheets is supposed to be calibrated so that the mean thickness μ of the sheets is more than 4 mm. The standard deviation of the sheet thicknesses is known to be well approximated by σ = 0.23 mm. Thicknesses of each sheet in a sample of sheets will be measured, and a test of the hypothesis H0 : μ ≤ 4 versus H1 : μ > 4 will be performed. Assume that, in fact, the true mean thickness is 4.04 mm. Section 06.07 Exercise 06.a a) If 100 sheets are sampled, what is the power of a test made at the 5% level? The power of a test made at the 5% level is _____. b) How many sheets must be sampled so that a 5% level test has power 0.95? ______ sheets must be sampled so that a 5% level test has power 0.95.c) If 100 sheets are sampled, at what level must the test be made so that the power is 0.90? The test must be made at _____% level so that the power is 0.90. d) If 100 sheets are sampled and the rejection region is  X¯ ≥ 4.02, what is the power of the test?…

A random sample of n = 19 winter days in Denver gave a sample mean pollution index x1 = 43. Previous studies show that o1 = 10. For Englewood (a suburb of Denver), a random sample of n2 = 18 winter days gave a sample mean pollution index of x2 = 34. Previous studies show that o2 = 13. Assume the pollution index is normally distributed in both Englewood and Denver. Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter? Use a 1% level of significance. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: H1 H2 O Ho: H1 = l2; H1: H1 < µ2 (b) What sampling distribution will you use? What assumptions are you making? O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's…