Suppose we are testing the null hypothesis H0: μ = 16 against the alternative Ha: μ> 16 from a normal populationwith known standard deviation o=3. A sample of size 324 is taken. We use the usual z statistic as our test statistic.Using the sample, a z value of 2.21 is calculated. (Remember z has a standard normall distribution.)a) What is the p value for this test?b) Would the null value have been rejected if this was a 2% level test?ΟΝΟΥc) Would the null value have been rejected if this was a 1% level test?ΟΝΟΥd) What was the value of x calculated from our sample?

given data,hypothesis:H0:μ=16H1:μ>16σ=3n=324z=2.21

Answered: Suppose we are testing the null…

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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Suppose we are testing the null hypothesis H0: ? = 13 against the alternative Ha: ? > 13 from a normal population with known standard deviation ?=5. A sample of size 256 is taken. We use the usual z statistic as our test statistic. Using the sample, a z value of 2.636 is calculated. (Remember z has a standard normal distribution.)a) What is the p value for this test? b) Would the null value have been rejected if this was a 1% level test? YN c) Would the null value have been rejected if this was a 0.1% level test? YN d) What was the value of x calculated from our sample?
Consider a random sample of size n from a normal distribution with unknown mean u and unknown variance o?. Suppose the sample mean is X and the sample variance is S?. n = 16, the observed sample mean i is 8.9. the observed sample variance s? is 25 and 4o : 10.5. Suppose we now want to test Ho : o? = of versus H1 : o? + of. Which of these test statistics should we use? Select one: (n-1)s? W = of a. O b. Z %3D O c. T= S/n Let o = 36. What is the (appropriate) observed test statistic? Give answer to three decimal places. What is the p-value of the (appropriate) observed test statistic for testing Ho : o? = of versus H1 : o? + of you just computed? Give answer to three decimal places.
Suppose we are testing the null hypothesis H0: μ = 13 against the alternative Ha: μ < 13 from a normal population with known standard deviation σ=4. A sample of size 289 is taken. We use the usual z statistic as our test statistic. Using the sample, a z value of -2.33 is calculated. (Remember z has a standard normal distribution.)    c) Would the null value have been rejected if this was a 1% level test? Yes or No    d) What was the value of x calculated from our sample?
I need help with parts D and C only. Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with σ = 2.9%. A random sample of 10 bank stocks gave the following yields (in percents). 5.7   4.8   6.0   4.9   4.0   3.4   6.5   7.1   5.3   6.1 The sample mean is = 5.38%. Suppose that for the entire stock market, the mean dividend yield is μ = 4.1%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.1%? Use α = 0.01. (a) What is the level of significance? (Enter a number.)State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H0: μ = 4.1%; H1: μ > 4.1%; right-tailedH0: μ = 4.1%; H1: μ < 4.1%; left-tailed     H0: μ > 4.1%; H1: μ = 4.1%; right-tailedH0: μ = 4.1%; H1: μ ≠ 4.1%; two-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since n is large with…
This test statistic leads to a decision to... A.) reject the null B.) accept the null C.) fail to reject the null You wish to test the following claim (Ha) at a significance level of α=0.002α=0.002.      Ho:μ=55.6      Ha:μ>55.6You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=601n=601 with mean ¯x=57.1x¯=57.1 and a standard deviation of s=19.9s=19.9.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = ___________What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = ____________The p-value is... A.) less than (or equal to) αα B.) greater than α As such, the final conclusion is that... A.) There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 55.6. B.) There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than…
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If the t-statistic for a single sample t-test is 1.58, what can you conclude? a. The test is significant at an alpha level of .05. b. The sample size of the test was at least 30. c. The sample mean was larger than the population mean. d. The population standard deviation was smaller than the difference between the sample mean and the population mean.
In a test of hypothesis, the null hypothesis is that the population mean is greater than or equal to 37 and the alternative hypothesis is that the population mean is less than 37. The population has a normal distribution with variance of 10.6. The test is to be made at the 5% significance level. In order that the value of power at M₁ = 35. 27 to be 0.9, how large a sample do we need? O d. 20 O e. 38 O c. 6 O a. 31 O b. 63
Suppose we wanted to test the hypothesis that a control group of cancer patients (Group 1) would report higher mean pain ratings than an experimental group receiving special massage treatments (Group 2). Using the following information, compute a t statistic for independent groups: Group 1: Mean = 76.5 Standard deviation = 13.1 N =20 Group 2: Mean = 72.1 Standard deviation = 14.7 N =20 What are the degrees of freedom and the value of t? Write a null and alternative hypothesis, Using α = .01 for one-tailed test, is this t statistically significant?

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