Let X~ N(x, 16) and Y~ N(µy, 36). = = (i) Suppose we want to test Ho: μx 7 against H₁ μx = 8 at significance level a = 0.05, by drawing a sample of size n from the distribution of X. What is the type II error probability 3? (Your answer will involve n and the standard normal distribution.) (ii) What is the minimum sample size n needed in order to ensure 3 ≤ 0.05?
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- The average number of pounds of sliced ham ordered per customer at the deli where Dennis used to work was 1.4, but at his new job, the average of the 32 people who have ordered ham so far is 1.5 pounds, with a standard deviation of 0.3 pounds. a) Write the null and alternative hypotheses to test if the average amount of ham bought is higher at the new store. H0:μ= H1:μ> b) For α=0.025, find the rejection region in terms of z. [Write your answer with 2 decimal places.] R:z≥ c) What test statistic corresponds to an x¯ of 1.5 pounds? [Round your answer to 2 decimal places.] z= d) Should you reject the null hypothesis?A person read that the average number of hours and adult sleeps on Friday night to Saturday morning was 7.3 hours. The researcher feels that college students do not sleep 7.3 hours on average. The researcher randomly selected 17 students and found that on average they slept 8.5 hours. The standard deviation of the sample is 1.4 hours. At (alpha) = 0.01, is there enough evidence to say that college students do not sleep 7.3 hours on average? Assume that the population is approximately normally distributed. Use the critical value method and tables. A. State the hypotheses and identify the claim with the correct hypothesis. B. Find the critical value(s). C. Compute the test value. D. Make the decision. E. Summarize the results.Find the t values that form the boundaries of the critical region for a two-tailed test with α = 0.10 for a sample size of
- If the alpha level changed from a=0.05 to a=0.01, what happens to the critical region and ehat happens to the probability of type 1 errorA computer company stated that children uses their products 6.77 hours per week. You gathered 30 independent samples from a group of children using their products and obtained an average 7.8 hours per week, with a sample standard deviation of 2.9 hours and at alpha = 0.10, compute the critical valueA random sample of 24 local sociology graduates scored an average of 460 on the GRE advanced sociology test, with a standard deviation of 22. We wonder if this significantly different from the national average (µ = 445). a) Evaluate assumptions if we can use a t-test and summarize parameters and statistics. b) State the null hypothesis (i.e., H0) and the working hypothesis (i.e., H1). c) Establish the critical region for t-distributions at α=0.05 with a two-tailed test. d) Compute the test statistics (i.e., tobtained) and the corresponding probability (i.e., pvalue). e) Make a decision and interpret test results.
- The distribution of weights (in pounds) of male students at a college is approximatelynormal with an unknown mean u and with an approximate standard deviation x = 15.3 lb. Considerrandom samples of 16 male students and let X denote the variable for the average weights of randomsamples of 16 male students.(a) What is the standard error of X with samples of size 16?(b) What is the distribution of X with samples of size 16?(c) Determine the minimum sample size n to ensure that the margin of error, E, of a two-sidedconfidence interval for u is at most 5 lb at 95% level of confidence.Let X1, X2, …, Xn be a random sample from the Normal distribution N() (a) Using method of moments to estimate the parameters and . (b) Are those estimators unbiased?In an Omani factory, a machine that produces "W-product" has been set so that the true average diameter of the "W-product" it produces is 0.602 in. If its diameter is within 0.04 in. of this target value, this is acceptable. Suppose, however, that the setting has changed during the course of production, so that the products have normally distributed diameters with mean value 0.601 in. and standard deviation 0.002 in. What percentage of the "W-product" produced will not be acceptable
- To test H0: σ=2.1versus H1: σ<2.1, a random sample of size n=21 is obtained from a population that is known to be normally distributed. If the sample standard deviation is determined to be s=1.9, compute the test statistic. χ20 If the researcher decides to test this hypothesis at the α=0.05 level of significance, determine the critical value. Draw a chi-squared distribution and depict the critical region Will the researcher reject the null hypothesis? Why? Choose the correct answer below. A. Yes,because χ20<χ20.95. B. No, because χ20<χ20.95. C.No, because χ20>χ20.95. D. Yes, because χ20>χ20.95A snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.23. A dietician is asked to test this claim and finds that a random sample of 24 servings has a variance of 1.27. At α=0.10, is there enough evidence to reject the manufacturer's claim? Assume the population is normally distributed. (b) Find the critical value(s). I do not know how to calculate the critical value with my calculator. I have a TI83+.Sony would like to test the hypothesis that the average age of a PlayStation user (mu 1) is greater than the average age of an Xbox user (mu 2). A random sample of 36 PlayStation users had an average age of 34.2 years while a random sample of 30 Xbox users had an average age of 32.7 years. Assume that the population standard deviation for the age of PlayStation and Xbox users is 3.9 and 4.0 years, respectively. Sony would like to set alpha = 0.01. The critical value is ________ and the null hypothesis should _______. Select one: a. -2.33; be rejected. b. 2.33; not be rejected. c. 1.96; be rejected. d. 1.645; not be rejected.
