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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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A data set includes data from student evaluations of courses. The summary statistics are

n=88,

x=3.67,

s=0.52.

Use a

0.05

significance level to test the claim that the population of student course evaluations has a mean equal to

3.75.

Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.

# Hypothesis Testing of Student Evaluation Data

A data set includes data from student evaluations of courses. The summary statistics are as follows:
- Sample size ($n$) = 88
- Sample mean ($\bar{x}$) = 3.67
- Sample standard deviation ($s$) = 0.52

We use a 0.05 significance level to test the claim that the population of student course evaluations has a mean equal to 3.75. Assume that a simple random sample has been selected.

The task is to identify the null and alternative hypotheses, determine the test statistic, calculate the P-value, and state the final conclusion that addresses the original claim.

## What are the null and alternative hypotheses?

Options:

- **A.** $ H_0: \mu = 3.75 $
$ H_1: \mu > 3.75 $

- **B.** $ H_0: \mu = 3.75 $
$ H_1: \mu < 3.75 $

- **C.** $ H_0: \mu = 3.75 $
$ H_1: \mu \neq 3.75 $ ✔️

- **D.** $ H_0: \mu \neq 3.75 $
$ H_1: \mu = 3.75 $

The correct selection is option **C**, where the null hypothesis ($ H_0 $) states that the mean is equal to 3.75, and the alternative hypothesis ($ H_1 $) states that the mean is not equal to 3.75.

## Determine the Test Statistic

- Use the provided blue box to input the test statistic, and ensure to round to two decimal places as needed.

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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