Answered: A survey of 41 people was conducted to…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 7PPS

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A survey of 41 people was conducted to compare their self-reported height to their actual height. The difference between reported height and actual height was calculated.

You're testing the claim that the mean difference is greater than 1.

From the sample, the mean difference was 1.1, with a standard deviation of 0.54.

Calculate the test statistic, rounded to two decimal places

Test the claim that the mean GPA of night students is smaller than the mean GPA of day students at the 0.05 significance level.

The null and alternative hypothesis would be:

H0:μN≤μDH0:μN≤μD
H1:μN>μDH1:μN>μD

H0:μN=μDH0:μN=μD
H1:μN≠μDH1:μN≠μD

H0:μN≥μDH0:μN≥μD
H1:μN<μDH1:μN<μD

H0:pN=pDH0:pN=pD
H1:pN≠pDH1:pN≠pD

H0:pN≥pDH0:pN≥pD
H1:pN<pDH1:pN<pD

H0:pN≤pDH0:pN≤pD
H1:pN>pDH1:pN>pD

The test is:

left-tailed

two-tailed

right-tailed

The sample consisted of 80 night students, with a sample mean GPA of 2.55 and a standard deviation of 0.03, and 80 day students, with a sample mean GPA of 2.6 and a standard deviation of 0.06.

The test statistic is: (to 2 decimals)

The p-value is: (to 2 decimals)

Based on this we:

Fail to reject the null hypothesis
Reject the null hypothesis

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 + ...

Expert Solution

Step 1

Solution:

Given information:

$n = 41 s a m p l e s i z e x_{d} = 1.1 D i f f e r e n c e o f s a m p l e m e a n s_{d} = 0.54 D i f f e r e n c e o f s a m p l e s \tan d a r d d e v i a t i o n μ_{d} = 1 D i f f e r e n c e o f p o p u l a t i o n m e a n$