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

26 The table to the right shows the cost per ounce​ (in dollars) for a random sample of toothpastes exhibiting very good stain​ removal, good stain​ removal, and fair stain removal. At α=0.01​, can you conclude that the mean costs per ounce are​ different? Perform a​ one-way ANOVA test by completing parts a through d. Assume that each sample is drawn from a normal​ population, that the samples are independent of each​ other, and that the populations have the same variances. Very good stain removal Good stain removal Fair stain removal   0.37 0.75 0.60   0.49 2.66 1.18   0.33 0.46 0.46   1.64 0.33     0.50 0.58     0.41 1.39           ​(b) Identify the degrees of freedom for the numerator and for the​ denominator, determine the critical​ value, and determine the rejection region. The degrees of freedom for the​ numerator, d.f.N​, is ____ and the degrees of freedom for the​ denominator, d.f.D​, is _____ The critical…

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 food manufacturer claims that eating its new cereal as part of a daily diet lowers total blood cholesterol levels. The table shows the total blood cholesterol levels​ (in milligrams per deciliter of​ blood) of seven patients before eating the cereal and after one year of eating the cereal as part of their diets. Use technology to test the mean difference. Assume the samples are random and​ dependent, and the population is normally distributed. At α=0.05​, can you conclude that the new cereal lowers total blood cholesterol​ levels? Patient 1 2 3 4 5 6 7   Total Blood Cholesterol (Before) 215 225 235 240 255 260 225   Total Blood Cholesterol​ (After) 214 222 240 237 254 257 222         Let the blood cholesterol level before eating the cereal be population 1. Let the blood cholesterol level after eating the cereal be population 2. Identify the null and alternative​ hypotheses, where μd=μ1−μ2. Choose the correct…

The pressure of air (in MPa) entering a compressor is measured to be X = 8.5 ± 0.2, and the pressure of the air leaving the compressor is measured to be Y = 21.2 ± 0.3. The intermediate pressure is therefore measured to be P = √XY = 13.42 . Assume that X and Y come from normal populations and are unbiased. a) From what distributions is it appropriate to simulate values X* and Y*? b) Generate simulated samples of values X*, Y*, and P*. c) Use the simulated sample to estimate the standard deviation of P. d) Construct a normal probability plot for the values P*. Is it reasonable to assume that P is approximately normally distributed? e) If appropriate, use the normal curve to find a 95% confidence interval for the intermediate pressure.

A researcher suspects that the mean birth weights of babies whose mothers did not see a doctor before delivery is less than 3000 grams. The researcher states the hypotheses as H:x = 3000 grams H, x 3000 grams; He:x< 3000 grams, where x = the mean birth weights of the sample of babies whose mothers did not see a doctor before delivery. Ho: x < 3000 grams; H,:x = 3000 grams, where x = the mean birth weights of the sample of babies whose mothers did not see a doctor before delivery. Ho: = 3000 grams; H # 3000 grams, where = the true mean birth weights of all babies whose mothers did not see a doctor before delivery. Ho: i = 3000 grams; H:< 3000 grams, where = the true mean birth weights of all babies whose mothers did not see a doctor before delivery. O Ho : š == 3000 grams; H. x 3000 grams, where x = the mean birth weights of the sample of babies whose mothers did not see a doctor before delivery.

3) Suppose test scores are measured by the Gaussian Normal Distribution N(X,75,10) calculate the following. a) Pr(80 < X < 90) b) Pr(50 < X < 70) c) The 95 th percentile

The random variable x has a normal distribution with mean 50 and variance 9. Find the value of x, call it x0, such that: a) P(x ≤ xo) = 0.8413 b) P(x > xo) = 0.025 c) P(x > xo) = 0.95 d) P(41 ≤ x ≤ xo) = 0.8630

1. In the past, a chemical company produced 880 pounds of a certain type of plastic per day. Now, using a newly developed and less expensive process, the mean daily yield of plastic for the first 50 days of production is 871 pounds; the standard deviation is 21 pounds. Do the data provide sufficient evidence to indicate that the mean daily yield for the new process is less than that of the old procedure? (Use α=0.05) (d) Conclusion of the test above is Reject the null hypothesis and the mean daily yield for the new process is less than that of the old procedure. Reject the null hypothesis and the mean daily yield for the new process is not less than that of the old procedure. Do not reject the null hypothesis and the mean daily yield for the new process is less than that of the old procedure. Do not reject the null hypothesis and the mean daily yield for the new process is not less than that of the old procedure.