The average birth weight of a newborn baby in the USA is reported to be 7.5 lbs. A random sample of n = 200 newborn babies was taken in a southern state. It is found that their average birth weight was 7.32 lbs with a standard deviation 2.16 lbs. Let u denote the average birth weight in this state. Perform a statistical test at a a = 0.05 level of significance to see if the average birth weight in this state matches well with the national average. (a) State the null and alternative hypotheses. (b) Let X - μο Z = s/√n be the z-test statistic. What is the null distribution of Z under Ho? What is the distri- bution of Z if μ = 7.2 in fact? (c) Compute the observed Z test statistic. Specify the rejection rule and draw conclusion accordingly. (d) Obtain the corresponding p-value.
The average birth weight of a newborn baby in the USA is reported to be 7.5 lbs. A random sample of n = 200 newborn babies was taken in a southern state. It is found that their average birth weight was 7.32 lbs with a standard deviation 2.16 lbs. Let u denote the average birth weight in this state. Perform a statistical test at a a = 0.05 level of significance to see if the average birth weight in this state matches well with the national average. (a) State the null and alternative hypotheses. (b) Let X - μο Z = s/√n be the z-test statistic. What is the null distribution of Z under Ho? What is the distri- bution of Z if μ = 7.2 in fact? (c) Compute the observed Z test statistic. Specify the rejection rule and draw conclusion accordingly. (d) Obtain the corresponding p-value.
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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![The following problem explores the statistical testing of average birth weight of newborns:
4. The average birth weight of a newborn baby in the USA is reported to be 7.5 lbs. A random sample of \( n = 200 \) newborn babies was taken in a southern state. It is found that their average birth weight was 7.32 lbs with a standard deviation of 2.16 lbs. Let \( \mu \) denote the average birth weight in this state. Perform a statistical test at a \( \alpha = 0.05 \) level of significance to see if the average birth weight in this state matches well with the national average.
(a) State the null and alternative hypotheses.
(b) Let
\[
Z = \frac{\overline{X} - \mu_0}{s/\sqrt{n}}
\]
be the z-test statistic. What is the null distribution of \( Z \) under \( H_0 \)? What is the distribution of \( Z \) if \( \mu = 7.2 \) in fact?
(c) Compute the observed \( Z \) test statistic. Specify the rejection rule and draw conclusion accordingly.
(d) Obtain the corresponding p-value.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc58b2eee-5b79-4c9d-923b-d4e913d44dbe%2F721ac083-b633-4e0a-85d4-6d9d691de67c%2F9uabp54_processed.png&w=3840&q=75)
Transcribed Image Text:The following problem explores the statistical testing of average birth weight of newborns:
4. The average birth weight of a newborn baby in the USA is reported to be 7.5 lbs. A random sample of \( n = 200 \) newborn babies was taken in a southern state. It is found that their average birth weight was 7.32 lbs with a standard deviation of 2.16 lbs. Let \( \mu \) denote the average birth weight in this state. Perform a statistical test at a \( \alpha = 0.05 \) level of significance to see if the average birth weight in this state matches well with the national average.
(a) State the null and alternative hypotheses.
(b) Let
\[
Z = \frac{\overline{X} - \mu_0}{s/\sqrt{n}}
\]
be the z-test statistic. What is the null distribution of \( Z \) under \( H_0 \)? What is the distribution of \( Z \) if \( \mu = 7.2 \) in fact?
(c) Compute the observed \( Z \) test statistic. Specify the rejection rule and draw conclusion accordingly.
(d) Obtain the corresponding p-value.
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