### Hypothesis Testing Problems#### 1. **a.** A sample of \( n = 13 \) observations has a sample mean of \( \bar{x} = 2.879 \). If an assumed known standard deviation of \( \sigma = 0.325 \) is used, calculate the p-values for the hypothesis testing problems:- **(a)** \( H_0 : \mu = 3.0 \) versus \( H_A : \mu \neq 3.0 \).- **(b)** \( H_0 : \mu \geq 3.1 \) versus \( H_A : \mu < 3.1 \).**b.** A food manufacturer claims that at the time of purchase by a consumer the average age of its product is no more than 120 days. In an experiment to test this claim a random sample of 36 items are found to have ages at the time of purchase with a sample mean of \( \bar{x} = 122.5 \) days and a sample standard deviation of \( s = 13.4 \) days.- **(a)** Write down the null hypothesis and the alternative hypothesis that the experimenter should use for the test.- **(b)** For what values of the t-statistic does the experimenter accept the null hypothesis with a level of significance \( \alpha = 0.10 \)?- **(c)** Is the null hypothesis accepted or rejected with \( \alpha = 0.10 \)?- **(d)** Write down an expression for the p-value and estimate it.

Here AS PER POLICY I HAVE CALCULATED FIRST MAIN QUESTION . PLZ REPOST FOR QUESTION B

Answered: 1. A sample of n=13 observations has a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B. The mean braking distance for Make A is 43 feet. Assume the population standard deviation is 4.6 feet. The mean braking distance for Make B is 46 feet. Assume the population standard deviation is 4.5 feet. At α=0.10, can the engineer support the claim that the mean braking distances are different for the two makes of automobiles? Assume the samples are random and independent, and the populations are normally distributed. The critical value(s) is/are Find the standardized test statistic z for μ1−μ2.
A population has parameters u = 189.5 and o = 61.9. You intend to draw a random sample of size n = 113. What is the mean of the distribution of sample means? What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.)
Suppose the diameter of holes for a cable harness is known to have a mean of 1.4 inches. A random sample of size 12 yields an average diameter of 1.6525 inches and standard deviation of 0.16 inch. Given that the data set is normally distributed, does this mean that this group of cable harnesses is significantly smaller? Test at α = 0.05.
A sample of 50 earthquakes was found to have a sample mean of x ¯ = 1.184 and a sample standard deviation of s = 0.5864. Test the claim that the population of earthquakes has a mean magnitude greater than 1.00. Use a 0.01 significance level. Find the test statistic and critical value used for this test. Round to three decimal places.
A population has parameters μ = n = 191. 49.2 and o= = 55.3. You intend to draw a random sample of size What is the mean of the distribution of sample means? fx = What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.) Ox =
The body temperatures of a group of healthy adults have abell-shaped distribution with a mean of 98.36°F and a standard deviation of 0.58°F. Using the empirical rule, find each approximate percentage below. What is the approximate percentage of healthy adults with body temperatures within 2 standard deviations of the mean, or between 97.20°F and 99.52°F? What is the approximate percentage of healthy adults with body temperatures between 96.62°F and 100.10°F?
A population has parameters u = 239.9 and o = 18.4. You intend to draw a random sample of size n = 76. What is the mean of the distribution of sample means? What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.)
The braking ability was compared for two car models. Random samples of two cars were selected. The first random sample of size 64 cars yield a mean of 36 and a standard deviation of 8. The second sample of size 64 yield a sample mean of 33 and a standard deviation of 8. Do the data provide sufficient evidence to indicate a difference between the mean stopping distances for the two models? Use Alpha= 0.01. Ho: µ1 – µ2 = 0 vs. Ha: µ1 – µ2 + 0 .p-value = 0.0017. Reject Ho Но: Д, — м2 — 0 vs. Ha:M1 — M2 + 0. p-value — 0.034. Ассеpt Ho O Ho:µ1 – Hz Но: И — 2 — 0 vs. Ha:M, — нz + 0. p-value —D 0.0017. Ассept Ho Ho: H1 – U2 = 0 vs. Ha: µ1 – µ2 + 0. p-value = 0.034. Reject Ho
Suppose there are two different vaccines for Covid, Vaccine X and Vaccine Y. An interesting question is which vaccine has a higher 6-month antibody effectiveness quotient (6AEQ). To examine this we randomly select 78 recipients of vaccine X and 93 recipients on vaccine Y. The vaccine X recipients had a mean 6AEQ of x = 151. The vaccine Y recipients had a mean 6AEQ of y = 148. It is recognized that the true standard deviation of 6AEQ for vaccine X recipients is 0x = 8.7 while it is recognized that the true standard deviation of 6AEQ for vaccine Y recipients is dy = 11.5. The true (unknown) mean 6AEQ for vaccine X recipients is μx, while the true (unknown) mean 6AEQ for vaccine Y recipients is y. 6AEQ measurements are known to be a normally distributed. In summary: Type Sample Size Sample Mean Standard Deviation Vaccine X 78 Vaccine Y 93 151 148 8.7 11.5 a) Calculate the variance of the random variable X which is the mean of the 6AEQ measurements of the 78 vaccine X recipients.…
(b) The weight, in grams, of red beans in a can is normally distributed with mean u and standard deviation 7.6. Given that 5% of cans contains less than 200g, determine; (i) The value of µ. (ii) The percentage of cans that contains more than 225 g of beans. A factory produces two types of artificial lamp A and B. The mean durability of artificial lamp A is 850 hours and its standard deviation is 40 hours. While, mean durability of artificial lamp B is 820 hours and its standard deviation is 60 hours. Find the probbality of 35 artificial lamp A will have mean durabilirty at least 25 hours more than 45 artificial lamp B. (c)
Suppose there are two different vaccines for Covid, Vaccine X and Vaccine Y. An interesting question is which vaccine has a higher 6-month antibody effectiveness quotient (6AEQ). To examine this we randomly select 78 recipients of vaccine X and 93 recipients on vaccine Y. The vaccine X recipients had a mean 6AEQ of x = 151. The vaccine Y recipients had a mean 6AEQ of y = 148. It is recognized that the true standard deviation of 6AEQ for vaccine X recipients is o, = 9.7 while it is recognized that the true standard deviation of 6AEQ for vaccine Y recipients is o, = 10.5. The true (unknown) mean SAEQ for vaccine X recipients is ly, while the true (unknown) mean 6AEQ for vaccine Y recipients is 4,. 6AEQ measurements are known to be a normally distributed. summary: Sample Size Sample Mean Standard Deviation 9.7 Гуре Vaccine 78 151 Vaccine Y 93 148 10.5 What is the length of your 96% confidence interval for uy Hy ? ) If we used this data to test Hg: Hy - Hy =0 against the alternative H: uy…

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS

1. A sample of n=13 observations has a sample mean of x= 2.879. If an assumed known standard deviation of o = 0.325 is used, calculate the p-values for the hypothesis testing problems: (a) Ho : µ = 3.0 versus HA :H 3.0. (b) Ho : µ>3.1 versus HA :µ < 3.1. а.