HW#7_Q

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Apr 3, 2024

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GENG 2220 HW#7 Due: 3/20/2024 11:59 pm Name:_______________________________ Student #:_________________________________ 1) A type I error occurs if one rejects the null hypothesis when it is _______________ A) non-zero B) true C) false D) zero 2) A type II error occurs if one does not reject the null hypothesis when it is ______________ A) zero B) false C) non-zero D) true 3) A right-tailed test is used when 𝐻𝐻 0 : 𝜇𝜇 ≥ 𝑘𝑘 . A) True B) False 4) Determine whether the alternative hypothesis is left-tailed, right-tailed, or two-tailed. 𝐻𝐻 0 : 𝜇𝜇 = 89 𝐻𝐻 1 : 𝜇𝜇 ≠ 89 A) two-tailed B) left-tailed C) right-tailed 5) The null hypothesis states that there is no difference between a parameter and a specific value, or that there is no difference between two parameters. A) True B) False 6) Are the following statements 𝐻𝐻 0 : = 5 𝑎𝑎𝑎𝑎𝑎𝑎 𝐻𝐻 1 : ≠ 5 valid null and alternative hypotheses? A) Yes, these statements are two non-overlapping hypotheses and compare two parameters. B) Yes, these statements are two non-overlapping hypotheses and compare a parameter to a value. C) No, the alternative hypothesis cannot contain numeric values. D) No, there are no parameters contained in these statements. 7) Which type of alternative hypothesis is used in the figure below? A) H 1 : μ < k B) H 1 : μ > k C) H 1 : μ = k D) H 1 : μ ≠ k

GENG 2220 HW#7 Due: 3/20/2024 11:59 pm Name:_______________________________ Student #:_________________________________ 8) A new organic pest control formula is being tested on potato plants to see whether it can reduce the level of potato beetle infestation. The mean number of beetles per untreated plant is 9. It is hoped that the new formula may reduce this infestation rate. State the appropriate null and alternate hypotheses. A) H 0 : μ = 9, H 1 : μ < 9 B) H 0 : μ < 9, H 1 : μ = 9 C) H 0 : μ < 9, H 1 : μ > 9 D) H 0 : μ = 9, H 1 : μ ≠ 9 9) Using the z table, find the critical value (or values) for an α = 0.024 left -tailed test. A) -0.99 B) -2.26 C) -1.13 D) -1.98 10) The numerical value obtained from a statistical test is called the ________________ A) hypothesis B) critical value C) test value D) level of significance 11) A garden supplier claims that its new variety of giant tomato produces fruit with an mean weight of 37 ounces. A test is made of H 0 : μ = 37 versus H 1 : μ ≠ 37. The null hypothesis is rejected. State the appropriate conclusion. A) The mean weight is equal to 37 ounces. B) There is not enough evidence to conclude that the mean weight is 37 ounces. C) The mean weight is not equal to 37 ounces. D) There is not enough evidence to conclude that the mean weight differs from 37 ounces. 12) At a water bottling facility, a technician is testing a bottle filling machine that is supposed to deliver 250 milliliters of water. The technician dispenses 36 samples of water and determines the volume of each sample. The 36 samples have a mean volume of 𝑥𝑥̅ = 251.6 mL. The machine is out of calibration if the mean volume differs from 250 mL. The technician wants to perform a hypothesis test to determine whether the machine is out of calibration. The standard deviation of the dispensed volume is known to be σ = 4.0. Compute the value of the test statistic. 12) ______ A) 2.40 B) 0.27 C) 4.80 D) 0.40

GENG 2220 HW#7 Due: 3/20/2024 11:59 pm Name:_______________________________ Student #:_________________________________ 13) A test is made of H 0 : μ = 44 versus H 1 : μ ≠ 44. A sample of size n = 74 is drawn, and 𝑥𝑥̅ = 51. The population standard deviation is σ = 24. Compute the value of the test statistic z and determine if H 0 is rejected at the α = 0.01 level. A) 0.29, H 0 rejected B) 2.51, H 0 rejected C) 2.51, H 0 not rejected D) 0.29, H 0 not rejected 14) A report by the Gallup Poll stated that on average a woman contacts her physician 5.8 times a year. A researcher randomly selects 20 women and obtained these data. 3 4 6 3 6 3 2 3 4 5 5 2 3 2 0 4 4 3 3 4 At α = 0.05, can it be concluded that the average is still 5.8 visits per year? A) Yes. There is not enough evidence to reject the claim that the mean number of vists per year is 5.8. B) No. There is enough evidence to reject the claim that the mean number of vists per year is 5.8. C) There is not enough information to draw a conclusion. 15) A political strategist claims that 58% of voters in Madison County support his candidate. In a poll of 200 randomly selected voters, 104 of them support the strategist's candidate. At α = 0.05, is the political strategist's claim warranted? A) No, because the test value -2.24 is in the critical region. B) No, because the test value -1.01 is in the noncritical region. C) Yes, because the test value -2.24 is in the noncritical region. D) Yes, because the test value -1.72 is in the noncritical region. 16) A scientist claims that only 67% of geese in his area fly south for the winter. He tags 60 random geese in the summer and finds that 17 of them do not fly south in the winter. If α = 0.05, is the scientist's belief warranted? A) Yes, because the test value 0.77 is in the noncritical region. B) No, because the test value 0.85 is in the critical region. C) No, because the test value -0.77 is in the noncritical region. D) Yes, because the test value -0.85 is in the noncritical region.

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GENG 2220 HW#7 Due: 3/20/2024 11:59 pm Name:_______________________________ Student #:_________________________________ 17) The manager of a large company claims that the standard deviation of the time (in minutes) that it takes a telephone call to be transferred to the correct office in her company is 1.4 minutes or less. A random sample of 15 calls is selected, and the calls are timed. The standard deviation of the sample is 1.9 minutes. At α = 0.05, test the claim that the standard deviation is less than or equal to 1.4 minutes. Use the P-value method. A) Since P-value > 0.05, reject the null hypothesis. There is enough evidence to reject the claim that the standard deviation is less than or equal to 1.4 minutes. B) Since P-value < 0.05, reject the null hypothesis. There is enough evidence to reject the claim that the standard deviation is less than or equal to 1.4 minutes. C) Since P-value < 0.05, do not reject the null hypothesis. There is not enough evidence to reject the claim that the standard deviation is less than or equal to 1.4 minutes. D) Since P-value > 0.05, do not reject the null hypothesis. There is not enough evidence to reject the claim that the standard deviation is less than or equal to 1.4 minutes. 18) If the probability of a type II error in a hypothesis test is 0.40, and α = 0.08, then the power of this test is A) 0.08 B) 0.40 C) 0.92 D) 0.60 19) The power of a test measures the sensitivity of the test to detect a real difference in parameters if one actually exists. A) True B) False 20) How can the power of a test be increased? A) The power can be increased by adding samples until the desired α is obtained. B) The power can be increased by rejecting bad samples. C) The power can be increased by increasing α or by selecting a larger sample size. D) The power can be increased by reducing the sample size.

HW#7_Q

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