A study conducted in the automotive field states that more than 40% of vehicle engine failures are due to problems in the cooling system. To test this statement, a study is carried out on 70 vehicles and the critical region is defined as x < 26, where x is the number of vehicle engines that have problems in the cooling system. (use the normal approximation) a) Evaluate the probability of making a type I error, assuming that p = 0.4. b) Evaluate the probability of committing a type II error, for the alternative p = 0.3
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1.- A study conducted in the automotive field states that more than 40% of vehicle engine failures are due to problems in the cooling system. To test this statement, a study is carried out on 70 vehicles and the critical region is defined as x < 26, where x is the number of vehicle engines that have problems in the cooling system. (use the normal approximation)
a) Evaluate the probability of making a type I error, assuming that p = 0.4.
b) Evaluate the probability of committing a type II error, for the alternative p = 0.3.
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- 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 54.8 inches. This average is maintained by periodically testing random samples of 25 tennis balls. If the t-value falls between −t0.95 and t0.95, 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 56.3 inches and the standard deviation is 0.25 inch. Assume the bounce heights are approximately normally distributed. Is the company making acceptable tennis balls?1. (See Handout 1, Example 1). The life expectancy of a particular brand of lightbulb is normally distributed with a mean of 1500 hours and a standard deviation of 75 hours. We want to calculate the probability that a lightbulb will last more than 1440 hours. a) Calculate the critical z-score. b) Label the axis and shade the area under the curve that we are interested in. Hours z-score c) What is the probability that a lightbulb will last more than 1440 hours? d) What is the probability that a lightbulb will last less than 1440 hours?Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the x distribution is about 4.78. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows. 4.9 4.2 4.5 4.1 4.4 4.3 (i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x = s = (ii) Do the given data indicate that the population mean RBC count for this patient is lower than 4.78? Use ? = 0.05. (a) What is the level of significance?State the null and alternate hypotheses. H0: ? < 4.78; H1: ? = 4.78H0: ? = 4.78; H1: ? ≠ 4.78 H0: ? = 4.78; H1: ? < 4.78H0: ? = 4.78; H1: ? > 4.78H0: ? > 4.78; H1: ? = 4.78 (b) What sampling…
- A prescription allergy medicine is supposed to contain an average of 245 parts per million (ppm) of active ingredient. The manufacturer periodically collects data to determine if the production process is working properly. A random sample of 64 pills has a mean of 250 ppm with a standard deviation of 12 ppm. Let u denotes the average amount of the active ingredient in pills of this allergy medicine. The null and alternative hypotheses are as Ho: μ = 245, Hau #245. The level of significance is 1%. The t-test statistic is 3.33 with a P-value of 0.0014. What is the correct conclusion? The mean amount of active ingredient in pills of this allergy medicine is greater than 245 ppm. The mean amount of active ingredient in pills of this allergy medicine is equal to 250 ppm. The mean amount of active ingredient in pills of this allergy medicine is equal to 245 ppm. moon amount of active ingredient in pills of this allergy medicine is not equal to 245 ppm.Past research has indicated that the average age of death row inmates is 41 years old. researcher would like to determine if the average age has changed. She randomly selects 50 death row inma s and ds their average age to be 37 years old. The hypothesis the statistician wants to test is: a. Ho: µ=37 vs_ Ha: µ ± 41. b. Ho: µ=41 vs Ha: µ< 41. Ho: u = 41 vs. H: u 41 d. Ho: µ=37 vs_Ha: µ< 41. C. 2. If a player at a casino is playing roulette and betting on red, there is a 18 / 38 or 0.474 chance that he will win on any spin of the roulette wheel. If we take a random sample of 300 players betting on red, then p is the proportion of times that the player wins. What is the mean of the sampling distribution of p? t' a. b. What is the standard deviation (os) of the sampling distribution of p? c. If repeated samples of 300 players are taken, what would be the range of the sample proportion of players victories according to the 95 part of the 68-95-99.7 rule" pts) 3. The z statistic for a…A major credit card company is investigating whether the distribution of the number of credit cards used by its customers has changed from last year to this year. Customers are classified as using 1 card, 2 cards, or more than 2 cards. The company conducts a chi-square goodness-of-fit test to investigate whether there is a change in the distribution of number of cards used from last year to this year. The value of the chi-square test statistic was χ2=7.82χ2=7.82 with a corresponding pp-value of 0.02. Assuming the conditions for inference were met, which of the following is the correct interpretation of this pp-value?
- The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000 miles of driving) of cars of a particular model varies Normally with mean 90 mg/mi and standard deviation of 4 mg/mi. A company has 25 cars of this model in its fleet. Find the level L such that the probability that the average NOX + NMOG level bar x for the fleet greater than L is only 0.03? Round final answer to three decimals.Let x be a random variable that represents the pH of arterial plasma (l.e., acidity of the blood). For healthy adults, the mean of the x distribution is = 7.4.t A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 31 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.8 with sample standard deviations = 3.3. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood. A USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O Hg: u + 7.4; H,: = 7.4 O Hg: H = 7.4; H,: H > 7.4 O H,: H = 7.4; H,i 7.4; H,: H = 7.4 O H: = 7.4; H,: H# 7.4 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since the sample size is large a is known. O The standard normal, since the sample size is large and a is known. O The standard normal,…2. Suppose the chamber of commerce at Pyramid Lake advertises that the average length of trout caught at the lake is μ = 19 inches. However, a fishing magazine survey reported that for a random sample of 51 fish caught, the mean length was x = 18.5 inches with estimated standard deviation s = 3.2 inches. Do these data indicate that the average length of the trout caught at Pyramid Lake is less than μ = 10 inches? (Use α = 0.05)
- The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in thedusLove uo useful life (150,000 miles of driving) of cars of a particular model varies Normall/ih nean 80 mg/mi and standard deviation 4 mg/mi. A company has 25 cars of this model in its et find the level L such that the probability that the average NOX+NMOG level 7 for the fleet is greater than L is only 0.01. Give your answer to three decimal places.The annual rainfall in a certain region is modeled using the normal distribution shown below. The mean of the distribution is 36.5 cm and the standard deviation is 5.2 cm. In the figure, V is a number along the axis and is under the highest part of the curve. And, U and W are numbers along the axis that are each the same distance away from V. Use the empirical rule to choose the best value for the percentage of the area under the curve that is shaded, and find the values of U, V, and W. Percentage of total area shaded: (Choose one) ▼ 200 35 | 55 25 30 40 45 50 ( cm) Submit Continue |Privacy Center © 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use DIl S0 FB F7 esc F3Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the x distribution is about 4.64. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows. 4.9 4.2 4.5 4.1 4.4 4.3 (1) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x=| S= (ii) Do the given data indicate that the population mean RBC count for this patient is lower than 4.64? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Ο Hg: μ= 4.64; H1: μ 4.64 Ο Ηρ: μ> 4.64; H1: μ = 4.64 Ho: u = 4.64; H1: u * 4.64 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O…