A random sample of 30 one-year-olds in a large day care resulted in the following heights in inches. 25 32 35 25 30 26.5 26 25.5 29.5 32 30 28.5 30 32 28 31.5 29 29.5 30 34 29 32 27 28 33 28 27 32 29 29.5 a) Find the mean and standard deviation of the sample using technology b) Construct a 95% confidence interval for the mean height of one-year-olds by answering the following: i. State the point estimate for the confidence interval. Find the critical value to determine the margin of error for the confidence interval. iii. Find the margin of error for the confidence interval. iv. Find the lower boundary for the confidence interval. Find the upper boundary for the confidence interval. vi. State the 95% confidence interval for the mean height of one-year-olds. vii. Interpret the confidence interval in the context of the problem. At a = 0.05, can it be concluded that the average height differs from 29 inches? To answer this question, answer the following questions i. State the null and alternative hypothesis. Also, state the claim and mention whether it is one or two tailed test. Na ii. Calculate the test statistics for this hypothesis testing using the data above. iii. By drawing and labelling the proper distribution, find the p value. Compare the p value with the significance level and state whether the null hypothe rejected or not. State the result of the hypothesis testing.

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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Question

A random sample of 30 one-year-olds in a large day care resulted in the following heights in inches.

26.5 26

25.5

29.5

28.5

31.5 29

29.5

a) Find the mean and standard deviation of the sample using

technology

b) Construct a 95% confidence interval for the mean height of one-year-olds by answering the

following:

State the point estimate for the confidence interval.

Find the critical value to determine the margin of error for the confidence interval.

iii.

Find the margin of error for the confidence interval.

Find the lower boundary for the confidence interval.

Find the upper boundary for the confidence interval.

State the 95% confidence interval for the mean height of one-year-olds.

vii.

Interpret the confidence interval in the context of the problem.

At a = 0.05, can it be concluded that the average height differs from 29 inches? To answer this

question, answer the following questions

State the null and alternative hypothesis. Also, state the claim and mention whether it is

one or two tailed test.

Calculate the test statistics for this hypothesis testing using the data above.

iii.

By drawing and labelling the proper distribution, find the p value.

Compare the p value with the significance level and state whether the null hypothe

rejected or not.

State the result of the hypothesis testing.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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