5 A 1-proportion Z test of the hypotheses Ho: p= 0.5 versus Ha: p# 0.5 produces a p-value of 0.027. Which of the following must be true?I. A 90% confidence interval for the true proportion will not contain the value 0.5II. A 95% confidence interval for the true proportion will not contain the value 0.5III. A 98% confidence interval for the true proportion will not contain the value 0.5O Il onlyO l onlyO Il and III onlyO l and Il onlyO None of the aboveO 1, Il and III

The random variable X follows normal distribution. The given hypotheses indicates z-test for one…

Answered: A 1-proportion Z test of the hypotheses…

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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In a test of H0: μ = 8 versus Ha: μ ≠ 8, a sample of size 220 leads to a p-value of 0.034. Which of the following must be true? a. A 95% confidence interval for μ calculated from these data will not include μ = 8. b. At the 5% level is H0 is rejected, the probability of a Type II error is 0.034. c. The 95% confidence interval for μ calculated from these data will be centered at μ = 8. d. The null hypothesis should not be rejected at the 5% level. e. The sample size is insufficient to draw a conclusion with 95% confidence.
Based on your confidence interval from the previous problem, can you conclude that the mean permeability coefficient at 60∘60∘C differs from that at 61∘61∘C at the 0.05 level of significance? A. Yes, because the 95% confidence interval includes 0 B. No, because the 95% confidence interval includes 0 C. Yes, because the 95% confidence interval does not include 0 D. No, because the 95% confidence interval does not include 0 E. It is impossible answer this question only using the 95% confidence interval.
If the null hypothesis H0 : μ = 13.0 is rejected at α = 0.01 when a mean of 17.0 is obtained from a random sample, one could also say that : a. the 99% confidence interval for the population mean does not contain the value 13.0. b. the 99% confidence interval for the population mean contains the value 17.0 c. the 99% confidence interval for the population mean contains the value 17.0 d. the 1% confidence interval for the population mean does not contain the value 13.0.
(a)A random sample of 25 college males was obtained and each was asked to report their actual height and what they wished as their ideal height. A 95% confidence interval for µd = average difference between their ideal and actual heights was 0.8" to 2.2". Based on this interval, which one of the null hypotheses below (versus a two-sided alternative) can be rejected? all the above c. H0: µd = 1.5 H0: µd = 0.5 b. H0: µd = 1.0 H0: µd = 2.0 (b)Which of the following is a correct form of an alternate hypothesis for paired data? H1: μd = p H1: μ1 ≠ μ2 H1: μd > 0 H1: μ1 = μ2 (C)Which of the following is always the null hypothesis for two sample proportions? d. H0: p1 = 3 H0: p1 < μ2 H0: p1 ≠ p2 H0: p1 = p2
A 95% confidence interval for the population mean μ was calculated to be (–0.3, 10.2), and the 90% confidence interval on the same set of data was calculated to be (0.5, 9.4). Which one of the following would be a possible p-value for the hypotheses: Ho : μ = 0 versus H1 : μ ≠ 0 ? a) 0.0648 b)0.05 c)0.0162 d)0.0324 e)0.1296
3. In a random sample of 300 persons eating lunch at a Lexington pizzeria, 270 ordered pizza. a) Find and interpret a 95% confidence interval for the true proportion of people who eat pizza at this Lexington pizzeria? b) If we take 270/300 = 0.90 as an estimate of the corresponding true proportion, with what confidence can we assert that our error is less than 0.04?
An avid birdwatcher wants to know if the number of goslings per goose in his lake differs from the regional average of 2.58. He takes a random sample of geese, conducts a hypothesis test of H0: μ = 2.58 vs.Ha: μ ≠ 2.58, and obtains a p-value of 0.013. (a) What should you expect of a 95% confidence interval constructed from his data? ---- The interval should contain 2.58 The interval should not contain 2.58 The interval should contain 0 The interval should not contain 0 We cannot say anything about the interval because ---- the p-value is not less than the corresponding alpha. the p-value is less than the corresponding alpha. we cannot make a conclusion about a confidence interval just from a hypothesis test. . (b) Given his sample size what 74, what critical value would the birdwatcher use to make the 95% confidence interval? (3 decimal places)(c) The birdwatcher's friend says his geese have an average of 3.88 goslings, and the birdwatcher wants to know if that would be a reasonable…
In exploring possible sites for a convenience store in a large neighbourhood, the retail chain wants to know the proportion of ratepayers in favour of the proposal. If the estimate is required to be within 0.1 of the true proportion, would a random sample of size n = 100 from the council records be sufficient for a 95% confidence interval of this precision?
If the 95% confidence interval for a parameter µ is (3.1, 5.1) and the 99% confidence interval for µ is (2.8, 5.4).One wants to test the hypotheses H0: µ = 3 v.s. Ha: µ ̸= 3.a. Will H0: µ = 3 be rejected at significance level α = 0.05? Why or why not?b. Will H0: µ = 3 be rejected at significance level α = 0.01? Why or why not?
. A researcher collects a sample of 24 measurements from a population and wishes to find a 99% confidence interval for the population mean. What value should he use for t*? b. If he instead decides to use a 95% confidence interval, will the interval be wider or be narrower or stay the same? Why?
Under proper conditions, the test of H0 ∶ µ = 5 versus Ha ∶ µ ≠ 5 results in a P-value of 0.035. Which of the following are true? A. A 95% confidence interval for µ will include the value 5. B. A 99% confidence interval for µ will not include the value 5. C. A 99% confidence interval for µ will include the value 0. D. A 95% confidence interval for µ will not include the value 5. E. A 95% confidence interval for µ will include the value 0.
It was found that in a sample of 90 teenage boys, 70% of them have received speeding tickets. What is the 90% confidence interval of the true proportion of teenage boys who have received speeding tickets? Given the above information, how many boys must be sampled to be within 2% of true proportion in a 90% confidence interval? b. If no information is given for the proportion, how many boys must be sampled?

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