To test the belief that sons are taller than their fathers, a student randomly selects 13 fathers who have adult male children. She records the height of both the father and son in inches and obtains the following data. Are sons taller than their fathers? Use theα=0.01level of significance. Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.LOADING...Click the icon to view the table of data.Height ofFather, XiHeight of Son, Yi 71.576.672.776.268.671.170.372.266.667.772.172.667.967.869.268.771.770.471.569.673.270.868.565.069.264.3PrintDoneWhich conditions must be met by the sample for this test? Select all that apply. A.The sampling method results in an independent sample. B.The sample size must be large. C.The sample size is no more than 5% of the population size. D.The differences are normally distributed or the sample size is large. E.The sampling method results in a dependent sample.Letdi=Xi−Yi.Write the hypotheses for the test. H0:▼ mu Subscript d Baseline not equals 0μd≠0mu Subscript d Baseline equals 0μd=0mu Subscript d Baseline greater than 0μd>0mu Subscript d Baseline less than 0μd<0H1:▼ mu Subscript d Baseline equals 0μd=0mu Subscript d Baseline less than 0μd<0mu Subscript d Baseline not equals 0μd≠0mu Subscript d Baseline greater than 0μd>0Calculate the test statistic. t0=nothing(Round to two decimal places as needed.)Calculate the P-value. P-value=nothing(Round to three decimal places as needed.)Should the null hypothesis be rejected? ▼ RejectDo not rejectH0because the P-value is▼ greater thanless thanthe level of significance. There▼ isis notsufficient evidence to conclude that sons▼ are taller thanare the same height asare shorter thanare not the same height astheir fathers at the0.01level of significance.

Name: To test the belief that sons are taller than their fathers, a student
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Description: To test the belief that sons are taller than their fathers, a student randomly selects 13 fathers who have adult male children. She records the height of both the father and son in inches and obtains the following data. Are sons taller than their f

A t-test for two paired samples is a hypothesis test that attempts to make a claim about the…

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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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To test the belief that sons are taller than their fathers, a student randomly selects 13 fathers who have adult male children. She records the height of both the father and son in inches and obtains the following data. Are sons taller than their fathers? Use the

α=0.01

level of significance. Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.

Click the icon to view the table of data.

Height of Father, Xi	Height of Son, Yi
71.5	76.6
72.7	76.2
68.6	71.1
70.3	72.2
66.6	67.7
72.1	72.6
67.9	67.8
69.2	68.7
71.7	70.4
71.5	69.6
73.2	70.8
68.5	65.0
69.2	64.3

PrintDone

Which conditions must be met by the sample for this test? Select all that apply.

The sampling method results in an independent sample.

The sample size must be large.

The sample size is no more than 5% of the population size.

The differences are normally distributed or the sample size is large.

The sampling method results in a dependent sample.

Let

di=Xi−Yi.

Write the hypotheses for the test.

H0:

▼

mu Subscript d Baseline not equals 0μd≠0

mu Subscript d Baseline equals 0μd=0

mu Subscript d Baseline greater than 0μd>0

mu Subscript d Baseline less than 0μd<0

H1:

▼

mu Subscript d Baseline equals 0μd=0

mu Subscript d Baseline less than 0μd<0

mu Subscript d Baseline not equals 0μd≠0

mu Subscript d Baseline greater than 0μd>0

Calculate the test statistic.

t0=nothing

(Round to two decimal places as needed.)

Calculate the P-value.

P-value=nothing

(Round to three decimal places as needed.)

Should the null hypothesis be rejected?

▼

Reject

Do not reject

because the P-value is

▼

greater than

less than

the level of significance. There

▼

is not

sufficient evidence to conclude that sons

▼

are taller than

are the same height as

are shorter than

are not the same height as

their fathers at the

0.01

level of significance.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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