17. What is the test statistic and its distribution for the hypothesis test stated in the preamble of Section E?X₁ X ₂ − (μ₁ −μ²), I ~ t25– µ₂)–OTT=√² + $n1N₂– µ2)¸ TX₁ X ₂ − (µμ₁ −μ₂) I ~ t25--OT:-s² S²+n1N₂ĎHD Tt26ΟΤ,SD/√nX₁ – X₂ − (µ₁ − µ₂)-OT=T~ t26"S² S²+n1N₂= Section E: The IQ scores of a sample of 15 boys randomly selected from the population of fifteen year-old boys inVictoria were recorded, and the sample mean and sample standard deviation from this sample were 106 and 4,respectively. The IQ scores of a sample of 12 girls randomly selected from the population of fifteen year-old girls inVictoria were recorded, and the sample mean and sample standard deviation from this sample were 114 and 5,respectively. Let μ₁ denote the mean IQ score for fifteen year-old boys in Victoria and let µ₂ denote the mean IQ scorefor fifteen year-old girls in Victoria. Researchers want to test, at the 5% level of significance, the null hypothesis-Ho: M1- µ2 = −1 vs the alternative hypothesis Ha : µ₁ − µ₂ −1. Assume the population standard deviations ofthe two groups are equal and that the assumptions of a two-independent sample t-test are satisfied. Answer thefollowing questions.

It is given that For the IQ scores of sample of boys Mean = 106 Sample standard deviation = 4…

Answered: 17. What is the test statistic and its…

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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#2 A Rollercoaster’s auditors estimate that the average daily loss from those illegally riding without tickets is at least $300, but wants to determine the accuracy of this statistic. The company researcher takes a random sample of losses over 64 days and finds that = $298 and s = $25. a) Test at α = 0.05. Be sure you cover all steps: hypothesis, critical value, acceptance range, conclusion. b) (Unrelated to a’s results) Construct a 95% confidence interval of losses.
What potential problems should you look for in the univariate distributions of categorical and quantitative scores? could you check over this problem and tell me what I did wrong. Calculate an effect size (n2) for each of the three t ratios and interpret these. N^2 = t^2/ (t^2 +df) = 20/ (1.9 +20) = 0.91 N^2 = t^2/ (t^2 +df) = 20/ (1.6 +20) = 0.92 N^2 = t^2/ (t^2 +df) = 20/ (0.5 +20) + 20.5
13. Two tail test with t-calc = 1.831 and degrees of freedom = 48. p-value of the test is: a) 0.05 < p-value < 0.1 b) 0.1 < p-value < 0.2 c) 0.01 < p-value < 0.02 d) 0.02 < p-value < 0.05
7. has been found that the distribution of the diameters of these tomatoes is roughly bell-shaped with light-tails. In order to test whether a new growth hormone produces larger tomatoes, a botanist decides to conduct a hypothesis test. If u denotes the true mean of tomatoes with the growth hormone and u2 denotes untreated tomatoes, then her hypotheses are Ho : 41 = µ2 vs. HA : µ1 > 42. She randomly samples 6 tomatoes, applies the new growth hormone to 3 of them, and measures the following diameters (in cm). Suppose that a certain species of tomato plant has been extensively studied. It Experimental Group 12.7 13.4 13.9 Control Group 9.7 10.4 13.1 (a) Explain why the two-sample t-test is the appropriate hypothesis test for the botanist to perform. (b) Based on the two sample t-test, is there sufficient evidence to reject Ho in favour of HA at the a = 0.15 significance level?
3. (Sample size determination for hypothesis testing) Suppose that X₁,..., Xn N(μ, o2) and o² is known. We would like to test We consider the test statistic Ho: μ = po, and the critical region at significance level a 1- {=; C = T = X x; x > µo + %α² H : μ > μο· B(μ') = = (a) We write ß(µ') to be the probability of type II error given the true value of µ = µ'. Prove that 0 (za + 10 = 1²). where Þ(z) = P(Z ≤ z) is the cdf of Z ~ N(0,1). 1 n = = O 2.2.d. (b) We would like to determine the sample size n so that the probability of type I error is a and the probability of type II error is ß. Using part (a), prove that 2 - ( 0¹ (²0 + zp)) ². Po - (c) Let u denote the true average tread life of a certain type of tire. Consider testing Ho : μ = 25,000 versus H₁ : μ> 25, 000 from a normal population distribution with o = 1300. Assuming the true value of μ is μ' = 24,000. What is the sample size n so that the probability of type I error is a = 0.05 and the probability of type II error is = 0.025?
the last question without the green check
The Natural Cereal Company claims that the average weight of is cereal boxes is at least 15oz. If a random sample of 24 boxes produced a sample mean x = 13.8 and a sample standard deviation s = 4.8, use the sample mean and standard deviation to test the claim at the 95% (? = 0.05) significance level. Use the hypothesis H0: μ = 15 and H1: μ < 15 with a one-tail test. Find the critical value for this confidence level. Find the T score for the tes statistic x=13.8.Based on the above T score – should you REJECT the null hypothesis H0?
11
We wish to test the null hypothesis that the proportion of cancer deaths among people exposed to radioactive fallout in Utah in 1955 is equal to 0.15 versus the alternative hypothesis that the proportion differs from 0.15 using alpha = 0.05. What is the region of rejection for this test for sample of size 20? Reject Ho if y in { LISTY VALUES HERE }
Calculate the test statistic x'and state your decision regarding the null hypothesis. 23. It has been rumored that the color distribution of M&M's is 30% brown, 20% yellow, 20% red, 10% orange, 10% blue, and 10% green. You suspect this rumor is incorrect and decide to count how many of each color are contained in a randomly chosen bag in order to perform a Chi-Square goodness-of-fit test at a 5% significance level. Color Brown Yellow Red Orange Blue Green Total Observed 27 16 21 12 15 100 Provided the assumptions of the test are satisfied, calculate the test statistic 7. a) 4.15, Reject H, b) 4.15, Fail to Reject H, c) 16.83, Reject H, d) 16.83, Fail to Reject H,

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