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When sample sizes are not equal, the non centrality parameter is
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Probability and Statistics for Engineering and the Sciences
- Assume X_1, X_2, .....X_n are random samples from X~Exponential(θ).1) Find the MLE estimator of θ .arrow_forwardIn a test of H0:p=0.4 against Ha:p≠0.4, a sample of size 100 produces z=1.28 for the value of the test statistic. Thus the p-value of the test is approximately equal to?arrow_forwardThe test statistic of z= - 1.56 is obtained when testing the claim that p < 0.51. A) using a significance level a=0.01, find the critical value’sarrow_forward
- A synthetic jewelry producer reports that a new procedure is only profitable if the average weight of the resulting diamonds is greater than 0.4 karat. She created six sample diamonds out of the new procedure and recorded their weights as follows: 0.36, 0.41, 0.42, 0.38, 0.47, and 0.34 karat. Do the six measurements present sufficient evidence to indicate that the new process is profitable? Test at 0.01 level of significance using the p-value method.arrow_forwardThe test statistic of z=−1.76 is obtained when testing the claim that p<0.85. a. Using a significance level of α=0.10, find the critical value(s). b. Should we reject H0 or should we fail to reject H0?arrow_forwardo test H0: μ=40 versus H1: μ<40, a random sample of size n=25 is obtained from a population that is known to be normally distributed. If x=37.1 and s=14.8, compute the test statistic of t0 and If the researcher decides to test this hypothesis at the α=0.1 level of significance, determine the critical value.arrow_forward
- The test statistic of Z equals=−2.06 is obtained when testing the claim that p<0.58 Using a significance level of α=0.01 find the critical value(s).arrow_forwardThe 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.arrow_forwardTo achieve statistical significance for a one-sample t-test, is which of the following? the t-obtained must be less than the t-critical. the t-obtained must be larger than the t-critical (farther into the region of rejection). the t-obtained must differ from the t-critical by .05. the t-obtained must equal the t-critical.arrow_forward
- A student makes ten measurements of the density of a gas (g/L) at a reduced pressure of 10.00 kPa and obtains the following values: 0.189, 0.167, 0.187, 0.183, 0.186, 0.182, 0.181, 0.184, 0.181, 0.177 From the list of values above, the most likely candidate is .... Based on a standard Q test, the calculated Q value for this entry is.......arrow_forwardThe midterm exam scores (X) and final exam scores (Y ) for a sample of students are related by the formula Y = aX + C, where X and Y are independent normal random variables.Assume that C has a zero mean and unknown standard deviation σ. Some statistics of the samples are mean of x=15 s.d. of x=5 mean of y=35 s.d. of y=2 Assuming that the actual statistics of X and Y are equal to the statistics of the sample, calculate the parameters a and σ.arrow_forwardIn a survey of 180 females who recently completed high school, 75% were enrolled in college. In a survey of 160 males who recently completed high school, 70% were enrolled in college. At α=0.07, can you reject the claim that there is no difference in the proportion of college enrollees between the two groups? Assume the random samples are independent. Complete parts (a) through (e). Find the critical value(s) and identify the rejection region(s).arrow_forward
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