# CED 6030, section 02, Fall 2015 Week 8 Assignment (Homework)

Question

11/16/2015 Week 8 Assignment

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Current Score : – / 51 Due : Wednesday, November 18 2015 11:59 PM EST

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In general, are chisquare distributions symmetric or skewed? If skewed, are they skewed right or

left?

skewed left

symmetric

skewed right

skewed right or left

1. –/1 pointsBBUnderStat11 10.1.001.

For chisquare distributions, as the number of degrees of freedom increases, does any skewness

increase or decrease? Do chisquare distributions become more symmetric (and normal) as the

number of degrees of freedom becomes larger and larger?

increases? no

decreases? yes

increases? yes

decreases? no

2. –/1 pointsBBUnderStat11 10.1.002.

Week 8 Assignment (Homework)

CED 6030, section 02, Fall 2015

WebAssign

11/16/2015 Week 8 Assignment

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For chisquare tests of independence and of homogeneity, do we use a righttailed, lefttailed, or

twotailed test?

twotailed

righttailed

lefttailed

righttailed or lefttailed

3. –/1 pointsBBUnderStat11 10.1.003.

In general, how do the hypotheses for chisquare tests of independence differ from those for chisquare

tests of homogeneity? Explain your answer.

The null for independence claims all the variables are independent whereas the null for

homogeneity claims a different proportion of interest from each population.

The null for independence claims all the variables are independent whereas the null for

homogeneity claims an equal proportion of interest from each population.

The null for homogeneity claims all the variables are independent whereas the null for

independence claims an equal proportion of interest from each population.

The null for independence claims all the variables are dependent whereas the null for

homogeneity claims an equal proportion of interest from each population.

4. –/1 pointsBBUnderStat11 10.1.004.

11/16/2015 Week 8 Assignment

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The following table shows site type and type of pottery for a random sample of 628 sherds at an

archaeological location.

Pottery Type

Site Type

Mesa Verde

BlackonWhite

McElmo

BlackonWhite

Mancos

BlackonWhite

Row Total

Mesa Top 78 58 53 189

CliffTalus 76 73 64 213

Canyon Bench 91 73 62 226

Column Total 245 204 179 628

Use a chisquare test to determine if site type and pottery type are independent at the 0.01 level

of significance.

(a) What is the level of significance?

State the null and alternate hypotheses.

H0: Site type and pottery are not independent.

H1: Site type and pottery are independent.

H0: Site type and pottery are independent.

H1: Site type and pottery are independent.

H0: Site type and pottery are not independent.

H1: Site type and pottery are not independent.

H0: Site type and pottery are independent.

H1: Site type and pottery are not independent.

(b) Find the value of the chisquare statistic for the sample. (Round the expected

frequencies to at least three decimal places. Round the test statistic to three decimal

places.)

Are all the expected frequencies greater than 5?

Yes

No

What sampling distribution will you use?

chisquare

Student’s t

5. –/9 pointsBBUnderStat11 10.1.011.

11/16/2015 Week 8 Assignment

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binomial

normal

uniform

What are the degrees of freedom?

(c) Find or estimate the Pvalue of the sample test statistic. (Round your answer to three

decimal places.)

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null

hypothesis of independence?

Since the Pvalue > ?, we fail to reject the null hypothesis.

Since the Pvalue > ?, we reject the null hypothesis.

Since the Pvalue ? ?, we reject the null hypothesis.

Since the Pvalue ? ?, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 1% level of significance, there is sufficient evidence to conclude that site and

pottery type are not independent.

At the 1% level of significance, there is insufficient evidence to conclude that site

and pottery type are not independent.

For a chisquare goodnessoffit test, how are the degrees of freedom computed?

The number of categories minus two.

The number of categories plus one.

The number of categories minus one.

The number of categories minus three.

6. –/1 pointsBBUnderStat11 10.2.001.

11/16/2015 Week 8 Assignment

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How are expected frequencies computed for goodnessoffit tests?

Divide the total sample size by the sample size for each category.

Take the proportion of the sample size for each category designated by the proposed

distribution.

Divide the proportion of the sample size for each category by the total sample size.

Take the proportion of the sample size for each category from the observed data.

7. –/1 pointsBBUnderStat11 10.2.002.

Explain why goodnessoffit tests are always righttailed tests.

We use a ?2 distribution where only smaller values can lead to rejecting the null.

We use a binomial distribution where only larger values can lead to rejecting the null.

We use a ?2 distribution where only larger values can lead to rejecting the null.

We use a normal distribution where only larger values can lead to rejecting the null.

8. –/1 pointsBBUnderStat11 10.2.003.

11/16/2015 Week 8 Assignment

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When the sample evidence is sufficient to justify rejecting the null hypothesis in a goodnessoffit

test, can you tell exactly how the distribution of observed values over the specified categories

differs from the expected distribution? Explain your answer.

Yes. When we reject the null, we can only conclude that the observed distribution is

different from the expected distribution.

No. When we reject the null, we can only conclude that the observed distribution is different

from the expected distribution.

Yes. When we reject the null, we can tell exactly how the observed distribution is different

from the expected distribution.

No. When we reject the null, we can tell exactly how the observed distribution is different

from the expected distribution.

9. –/1 pointsBBUnderStat11 10.2.004.

11/16/2015 Week 8 Assignment

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The type of household for the U.S. population and for a random sample of 411 households from a

community in Montana are shown below.

Type of Household

Percent of U.S.

Households

Observed Number

of Households in

the Community

Married with children 26% 104

Married, no children 29% 118

Single parent 9% 30

One person 25% 90

Other (e.g., roommates, siblings) 11% 69

Use a 5% level of significance to test the claim that the distribution of U.S. households fits the

Dove Creek distribution.

(a) What is the level of significance?

State the null and alternate hypotheses.

H0: The distributions are the same.

H1: The distributions are the same.

H0: The distributions are the same.

H1: The distributions are different.

H0: The distributions are different.

H1: The distributions are the same.

H0: The distributions are different.

H1: The distributions are different.

(b) Find the value of the chisquare statistic for the sample. (Round the expected

frequencies to two decimal places. Round the test statistic to three decimal places.)

Are all the expected frequencies greater than 5?

Yes

No

What sampling distribution will you use?

Student’s t

10.–/9 pointsBBUnderStat11 10.2.006.

11/16/2015 Week 8 Assignment

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binomial

uniform

normal

chisquare

What are the degrees of freedom?

(c) Find or estimate the Pvalue of the sample test statistic. (Round your answer to three

decimal places.)

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null

hypothesis that the population fits the specified distribution of categories?

Since the Pvalue > ?, we fail to reject the null hypothesis.

Since the Pvalue > ?, we reject the null hypothesis.

Since the Pvalue ? ?, we reject the null hypothesis.

Since the Pvalue ? ?, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, the evidence is sufficient to conclude that the

community household distribution does not fit the general U.S. household

distribution.

At the 5% level of significance, the evidence is insufficient to conclude that the

community household distribution does not fit the general U.S. household

distribution.

11/16/2015 Week 8 Assignment

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Does the x distribution need to be normal in order to use the chisquare distribution to test the

variance? Is it acceptable to use the chisquare distribution to test the variance if the x

distribution is simply moundshaped and more or less symmetric?

Yes, it needs to be normal. No, the chisquare test of variance requires the x distribution to

be exactly normal.

No, it does not need to be normal. Yes, the chisquare test of variance allows for the x

distribution to be simply moundshaped or symmetric.

Yes, it needs to be normal. Yes, the chisquare test of variance allows for the x distribution

to be simply moundshaped or symmetric.

No, it does not need to be normal. No, the chisquare test of variance requires the x

distribution to be exactly normal.

11.–/1 pointsBBUnderStat11 10.3.001.

11/16/2015 Week 8 Assignment

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Let x = age in years of a rural Quebec woman at the time of her first marriage. In the year 1941,

the population variance of x was approximately ?2 = 5.1. Suppose a recent study of age at first

marriage for a random sample of 31 women in rural Quebec gave a sample variance s2 = 2.5. Use

a 5% level of significance to test the claim that the current variance is less than 5.1. Find a 90%

confidence interval for the population variance.

(a) What is the level of significance?

State the null and alternate hypotheses.

Ho: ?2 = 5.1? H1: ?2 ? 5.1

Ho: ?2 5.1

Ho: ?2 = 5.1? H1: ?2 ?2

2

H0: ?1

2 = ?2

2? H1: ?1

2 ? ?2

2

H0: ?1

2 = ?2

2? H1: ?1

2 ?2

2? H1: ?1

2 = ?2

2

(b) Find the value of the sample F statistic. (Round your answer to two decimal places.)

What are the degrees of freedom?

dfN =

dfD =

What assumptions are you making about the original distribution?

The populations follow dependent normal distributions. We have random samples

from each population.

The populations follow independent normal distributions. We have random samples

from each population.

The populations follow independent chisquare distributions. We have random

samples from each population.

The populations follow independent normal distributions.

17.–/9 pointsBBUnderStat11 10.4.012.

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(c) Find or estimate the Pvalue of the sample test statistic. (Round your answer to four

decimal places.)

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null

hypothesis?

At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not

statistically significant.

At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are

statistically significant.

At the ? = 0.05 level, we reject the null hypothesis and conclude the data are

statistically significant.

At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are

not statistically significant.

(e) Interpret your conclusion in the context of the application.

Reject the null hypothesis, there is sufficient evidence that the population variance

is smaller in the new thermostat temperature readings.

Fail to reject the null hypothesis, there is insufficient evidence that the population

variance is smaller in the new thermostat temperature readings.

Fail to reject the null hypothesis, there is sufficient evidence that the population

variance is smaller in the new thermostat temperature readings.

Reject the null hypothesis, there is insufficient evidence that the population variance

is smaller in the new thermostat temperature readings.

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