The following table shows the Myers-Briggs personality preferences for a random sample of 406 people in the listed professions. E refers to extroverted and I refers to introverted.

Clergy (all denominations ) 63 44 107

M.D. 67 95 162

Lawyer 52 85 137

Column Total 182 224 406

Find or estimate theP-value of the sample test statistic.

p-value > 0.100

0.050 <p-value < 0.100

0.025 <p-value < 0.050

0.010 <p-value < 0.025

0.005 <p-value < 0.010

p-value < 0.005

Mr. Acosta, a sociologist, is doing a study to see if there is a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred. A random sample of 93 adults revealed the following data. Test whether age and type of movie preferred are independent at the 0.05 level.

Person's Age

Movie 18-23 yr 24-29 yr 30-35 yr Row Total

Drama 7 12 15 34

Science Fiction 10 8 12 30

Comedy 10 6 13 29

Column Total 27 26 40 93

Find or estimate theP-value of the sample test statistic.

P-value > 0.100

0.050 <P-value < 0.100

0.025 <P-value < 0.050

0.010 <P-value < 0.025

0.005 <P-value < 0.010

P-value < 0.005

The age distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of a village are shown below.

Age (years) Percent of Canadian Population Observed Number

in the Village

Under 5 7.2% 42

5 to 14 13.6% 74

15 to 64 67.1% 297

65 and older 12.1% 42

A) 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 chi-square statistic for the sample. (Round your answer to three decimal places.)

What are the degrees of freedom?

(c) Estimate theP-value of the sample test statistic.

P-value > 0.100

0.050 <P-value < 0.100

0.025 <P-value < 0.050

0.010 <P-value < 0.025

0.005 <P-value < 0.010

P-value < 0.005

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 theP-value >, we fail to reject the null hypothesis.

Since theP-value >, we reject the null hypothesis.

Since theP-value, we reject the null hypothesis.

Since theP-value, we fail to reject the null hypothesis.

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% 100

Married, no children 29% 121

Single parent 9% 35

One person 25% 88

Other roommates, siblin 11% 67

State the null and alternate hypotheses.

H₀: The distributions are the same.H₁: The distributions are the same.

H₀: The distributions are different.H₁: The distributions are different.

H₀: The distributions are different.H₁: The distributions are the same.

H₀: The distributions are the same.H₁: The distributions are different.

(b)

Find the value of the chi-square statistic for the sample. (Round the expected frequencies to two decimal places. Round the test statistic to three decimal places.)

Find or estimate the P-value 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 P-value > , we fail to reject the null hypothesis.

Since the P-value > , we reject the null hypothesis.

Since the P-value , we reject the null hypothesis.

Since the P-value , we fail to reject the null hypothesis.

The types of raw materials used to construct stone tools found at an archaeological site are shown below. A random sample of 1486 stone tools were obtained from a current excavation site.

Raw Material Regional Percent of Stone Tools Observed Number of Tools as Current excavation Site

Basalt 61.3% 893

Obsidian 10.6% 165

Welded Tuff 11.4% 179

Pedernal 13.1% 198

Other 3.6% 51

Use a 1% level of significance to test the claim that the regional distribution of raw materials fits the distribution at the current excavation site.

(a) What is the level of significance?

State the null and alternate hypotheses.

H0: The distributions are different.

H1: The distributions are different.

H0: The distributions are the same.

H1: The distributions are different.

H0: The distributions are the same.

H1: The distributions are the same.

H0: The distributions are different.

H1: The distributions are the same.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

(c) Find or estimate the P-value of the sample test statistic.

P-value > 0.100

0.050 < P-value < 0.100

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

P-value < 0.005

The types of browse favored by deer are shown in the following table. Using binoculars, volunteers observed the feeding habits of a random sample of 320 deer.

Type of Browse Plant Composition

in Study Area Observed Number of Deer

Feeding on This Plant

Sage brush 32% 98

Rabbit brush 38.7% 134

Salt brush 12% 38

Service berry 9.3% 27

Other 8% 23

Use a 5% level of significance to test the claim that the natural distribution of browse fits the deer feeding pattern.

(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 different.

H1: The distributions are different.

H0: The distributions are the same.

H1: The distributions are different.

H0: The distributions are different.

H1: The distributions are the same.

(b) Find the value of the chi-square 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?

uniform

normal

chi-square

binomial

Student's t

What are the degrees of freedom?

(c) Estimate the P-value of the sample test statistic.

P-value > 0.100

0.050 < P-value < 0.100

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

P-value < 0.005

(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 P-value > , we fail to reject the null hypothesis.

Since the P-value > , we reject the null hypothesis.

Since the P-value , we reject the null hypothesis.

Since the P-value , 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 natural distribution of browse does not fit the feeding pattern.

At the 5% level of significance, the evidence is insufficient to conclude that the natural distribution of browse does not fit the feeding pattern.

The Fish and Game Department stocked a lake with fish in the following proportions: 30% catfish, 15% bass, 40% bluegill, and 15% pike. Five years later it sampled the lake to see if the distribution of fish had changed. It found that the 500 fish in the sample were distributed as follows.

Catfish Bass Bluegill Pike

124 93 198 85

State the null and alternate hypotheses.

H0: The distributions are the same. H1: The distributions are different.

H0: The distributions are different. H1: The distributions are different.

H0: The distributions are the same. H1: The distributions are the same.

H0: The distributions are different. H1: The distributions are the same.

Estimate the P-value of the sample test statistic.

P-value > 0.100

0.050 < P-value < 0.100

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

P-value < 0.005

(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 P-value > , we fail to reject the null hypothesis.

Since the P-value > , we reject the null hypothesis.

Since the P-value , we reject the null hypothesis.

Since the P-value , we fail to reject the null hypothesis