Let x be hemoglobin count (HC) in grams per 100 milliliters of whole blood for a healthy adult woman. It is believed that x has a normal distribution with a mean of 14 and an unknownstandard deviation. A random sample of ten healthy adult females was taken with the following HC for each::15, 18, 16, 19, 14, 12, 14, 17, 15, 11So, we assume that our sample comes from a normal population with unknown standard deviation of o. We would like to test whether the mean HC is higher than 14.The null hypothesis is thus Ho:μ=14. We will test this against the alternative H₂.We want to test at the 1% level.Let x = the sample mean and s = the sample standard deviation. c) What value does your test statistic, T, take on with the sample data?d) What type of probability distribution does your test statistic, T, have?O Chi-SquaredOtO binomialO CauchyO normale) How many degrees of freedom does T have?f) Calculate the critical value, tstar, for your test.(positive value)g) For what values of your test statistic, T, is the null hypothesis rejected?O T tstar or T < -tstarOT > tstarOT> tstar/2 or T < -tstar/2h) Calculate the p-value for this test.i) Is the null hypothesis rejected? (Y/N)ΟΥONj) If we ran 800, 1% level tests then about how many times would we make a Type I error?k) Create a 99% confidence interval for the mean hemoglobin count (HC) in grams per 100 milliliters of whole blood for a healthy adult woman: (

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The following is a set of hypotheses, some information from one or more samples, and a standard error from a randomization distribution. Test Ho : p = 0.26 vs Ha : p < 0.26 when the sample has n = 700, and p = 0.215 with SE = 0.02. Find the value of the standardized z-test statistic. Round your answer to two decimal places. 3.1
The assumption of homogeneity of variances was tested by Levene’s Test, F(2, 432) = .75, p = .48. Was the assumption met?
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The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes with a sample standard deviation of 0.5 minutes. We want to determine whether or, not the mean waiting time of all customers is significantly different than 3 minutes. Then the correct set of hypotheses is Select one: Oa. HO: u 3 H1: u = 3.1 O b. HO: u = 3 H1: u # 3 %3D О с. НО: и 2 3 H1: u = 3 d. HO: u = 3.1 H1: u # 3
The average fees paid by students at state universities across the country were $2236 per student last year. The average for a random sample of 500 students this year is $2350. Given the following hypotheses, Ho: 4 = 2236 (The average fees are the same as last year.) Ha: H = 2236 (The average fees are not the same as last year.) Compute the p-value for the sample result. Assume the population standard deviation is $724. If the significance level is 5%, can the null hypothesis be rejected? A. none of these B. The p-value here is .04. Since .04 is less than the significance level, that is, since .04 < .05, we can reject HO C. The p-value here is .02. Since 02 is less than the significance level, that is, since 02 < 05, we can't reject HO. D. The p-value here is .0004. Since .0004 is less than the significance level, that is, since .0004 < .05, we can reject HO.
Grand Sun Buffet is a large restaurant chain. After paying for a meal at Grand Sun Buffet, customers are asked to rate the quality of the food as a 1, 2, 3, 4, or 5, where a rating of 1 means "not good" and 5 means "excellent". The customers' ratings have a population mean of u=4.57, with a standard deviation of o =1.82. Suppose that we will take a random sample of n=7 customers' ratings. Let x represent the sample mean of the 7 customers' ratings. Consider the sampling distribution of the sample mean x. Complete the following. Do not round any intermediate computations. Write your answers with two decimal places, rounding if needed. (a) Find u- (the mean of the sampling distribution of the sample mean). (b) Find o- (the standard deviation of the sampling distribution of the sample mean). D-
I. A study reports that teenagers spend 27 hours a week online (www.telegraph.co.uk). A researcher wanted to check if this claim is true. A random sample of 200 teenagers taken showed that they spend an average of 25.7 hours per week online with a standard deviation of 8.2 hours. Perform a hypothesis test with the alternate hypothesis that teenagers spend less than 27 hours per week online. Use c = 0.05. Perform all of the steps outline in your notes and write a complete conclusion in words. Assume the distribution of hours spent online is normally distributed.
We want to test hypotheses concerning the population mean. The following data is given: x¯¯¯=82,n=15, the population is normal with a standard deviation of 5.2. If we are to test the following hypothesis: H0:μ=85 Ha:μ<85 with a significance level of 0.05, the p-value suggests we a.) accept the alternate hypothesis b.) Fail to reject the null hypothesis c.) reject the null hypothesis d.) do nothing, let someone else get paid to figure it out.
If random samples, each with n = 16 scores, are selected from a normal population with µ = 100 and σ = 20, how much difference, on average, should there be between a sample mean and the population mean?
From a sample with n=36, the mean duration of a geyser's eruptions is 3.06 minutes and the standard deviation is 0.85 minutes. Using Chebychev's Theorem, determine at least how many of the eruptions lasted between 1.36 and 4.76 minutes. At least of the eruptions lasted between 1.36 and 4.76 minutes. (Simplify your answer.)
A test of sobriety involves measuring the subject's motor skills. Twenty randomly-selected sober subjects take the test and produce a mean score of 41.0 with a standard deviation of 3.7. At the 0.01 level of significance, test the claim that the true mean score for all sober subjects is equal to 35.0. Use the traditional method of testing hypotheses. The results for the test turn out to be: Ho: H = 35.0. H1:µ/35.0. Test statistic: t 7.252. Critical values: t = -2.861, 2.861. Reject Ho. There is sufficient evidence to warrant rejection of the claim that the mean is equal to 35.0. If a defense attorney argues the results are not valid because the sample size was too small, is his argument valid here? Yes, because the t-test is not as powerful as the z-test. No, because we rejected the null hypothesis. Yes, because we rejected the null hypothesis. O No, the sample size is never an issuc. O We need more information to answer.

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