3. If the 95% confidence interval for a parameter u is (3.1, 5.1) and the 99% confidence interval for u is(2.8, 5.4). One wants to test the hypotheses Ho: µ = 3 v.s. Ha: µ #3.Will Ho: u3 be rejected at significance level a == 0.05? Why or why not?Will Ho: µ =3 be rejected at significance level a =0.01? Why or why not?

For 95% confidence interval for mean is (3.1,5.1) that means the mean should lie between 3.1 and 5.1…

Answered: 3. If the 95% confidence interval for a…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 10E

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3. 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 6= 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?
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?
You wish to conduct a hypothesis test to determine if a bivariate data set has a significant correlation among the two variables. That is, you wish to test the claim that there is a correlation (H.:p7 0). а You have a data set with 5 subjects, in which two variables were collected for each subject. You will conduct the test at a significance level of a = 0.05. Find the critical value for this test. rc.v. Report answers accurate to three decimal places.
Suppose we are making predictions of the dependent variable y for specific values of the independent variable x using a simple linear regression model holding the confidence level constant. Let Width (C.I) = the width of the confidence interval for the average value y for a given value of x, and Width (P.I) = the width of the prediction interval for a single value y for a given value of x. Which of the following statements is true? Width (C.I) = 0.5 Width (P.I) Width (C.I) = Width (P.I) Width (C.I) > Width (P.I) Width (C.I) < Width (P.I)
A 95% confidence interval for the mean body mass index (BMI) of young American women is 26.8 ± 0.6. One of your classmates interprets this interval in the following way: "We are 95% confident that future samples of young women will have mean BMI between 26.2 and 27.4." Is your classmate's interpretation correct? If not, what is the correct interpretation of the confidence interval? Correct. This interpretation correctly refers to the parameter (all young women). Incorrect. We are 95% confident that the interval from 26.2 and 27.4 captures the true mean BMI of all young American women. Incorrect. If we take many samples, the population mean BMI will be between 26.2 and 27.4 in about 95% of those samples. Incorrect. The mean BMI of young American women cannot be 28. Incorrect. We are 95% confident that the interval from 26.2 and 27.4 captures the BMI for every young American woman.
Newspaper headlines recently announced a decline in science scores among high school seniors. In 2015, 15,109 seniors tested by The National Assessment in Education Program (NAEP scored a mean of 147 points. In 2000, 7537 seniors had averaged 150 points. The standard error of the difference in the mean scores for the two groups was 1.22. a) State the null and alternative hypotheses in terms of the appropriate parameter. Ho: p1 - µ2 HA: H1 - µ2 b) The point estimate is c) The test statistic is ? v . (If necessary, round your answer to the nearest hundredth.) d) The p-value is e) The correct decision is to Select an answer | the null hypothesis. f) There is Select an answer evidence that scores have decreased between 2000 and 2015. g) We are 95% confident that the mean score has decreased by between and points between 2000 and 2015. (If necessary, round your answers to the nearest hundredth.)
2. Two detergents were tested for their ability to remove stains. The first one was suc- cessful on 63 out of 91 trials and the second one was successful on 42 out of 79 trials. Construct approximated 95% one-sided confidence intervals for the difference pi – P2 where the successful rates are pi and p2, respectively.
Construct a 99% confidence interval for u, - u, with the sample statistics for mean cholesterol content of a hamburger from two fast food chains and confidence interval construction formula below. Assume the populations are approximately normal with unequal variances. Stats X, = 87 mg, s, = 3.77 mg, n, = 14 X, = 45 mg, s. = 2.24 mg, n, = 18 Confidence interval when (X, – X2) -te. variances are not equal +t. n n2 n2 d.f. is the smaller of n, -1 or n2-1 Enter the endpoints of the interval.
1. The following data, recorded in days, represents the recovery time „for patients who are randomly treated with one of two medications to cure severe bladder infections: Medication 1 Medication 2 n1 =13 n2 =16 1 =20 i2 =15 s =2.0 s, =1.8 Find the 99% confidence interval for u1- µ2, the difference in mean drug recovery times, and INTERPRET it to get a helpful conclusion about the drugs. Assume normal populations, with equal variances. As an answer to this question, enter the lower limit of the confidence interval found, rounded to two digits. For example, if the interval is [2.3923, 5.0579], enter 2.39. IMPORTANT: Please put all procedure and please include the Correct INTERPRETATION of the confidence interval. THANKS I
Construct a 90% confidence interval for u, - Ho with the sample statistics for mean cholesterol content of a hamburger from two fast food chains and confidence interval construction formula below. Assume the populations are approximately normal with unequal variances. Stats X = 122 mg, s, = 3.72 mg, n, = 12 X2 = 51 mg, s, =2.17 mg, n2 = 14 %3D %3D Confidence interval when (X1 – X2) -t variances are not equal
5. Consider the following estimated equation that is used to study the effect of skipping class on colege GPA: COLGPA- 1.39+412 HSGPA+015 ACT - 083 skipped (011) (.026) (33) (.094) n= 141, R2= 234 (1) Using the standard normal approximation, find the 95% confidence interval for puA (2) Based on the 95% confidence interval you obtained, can you reject the hypothesis H BOPA = 0.4 against the two-sided alternative at the 5% level? (3) Can you reject the hypothesis H: PPA = 0.1 at the 5% level? (4) Can you reject the hypothesis H,: P 0.8 at the 5% level?
Let's examine the relationship between CI's and hypothesis tests: (a) You calculate a 90% confidence interval for μ and come up with (-26, 10). If you test H0: μ = -7 and use α = .10, will you reject H0? Why or why not? (b) Now you calculate a 95% CI for μ and come up with (-5, -1). If you test H0: μ = 0 and use α = .10, will you reject H0? Why or why not? (c) Finally, you calculate a 95% CI for for μ and come up with (-24, -8). If you test H0: μ = - 13 and use α = .01, will you reject H0? Why or why not?

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