# Hypothesis and identifying a Claim

a. State the hypotheses and identify the claim

b. Find the critical value

c. Compute the test value

d. Make the decision

e. summarize the results and explain where the differences in the mean are

Question # 1 Number of State Parks The number of state parks found in selected states in three different regions of the country are listed below at a = 0.05 can it be concluded that the average number of state parks differ by region

South West New England

51 28 94

64 44 72

35 24 14

24 31 52

47 40

Question # 2 Grams of fat per serving of pizza. The number of grams of fat per serving for three different kinds of pizza from several manufacturers is listed below. At the 0.01 level of significance, is there sufficient evidence that a difference exists in the mean fat content?

Cheese Pepperoni Supreme/Deluxe

18 20 16

11 17 27

19 15 17

20 18 17

16 23 12

21 23 27

16 21 20

Question # 3

Information Gathering and Educational Background. An instructor wishes to see if the way people obtain information is independent of their educational background. A survey of 400 high school and college graduates yielded this information. At a = 0.05, test the claim that the way people obtain information is independent of their educational background.

Television Newspaper Other Sources

High school 159 90 51

College 27 42 31

Question #4

Effectiveness of a new drug to test the effectiveness of a new drug, a researcher gives one group of individuals the new drug and another group a placebo. The results of the study are shown here at a = 0.10 can the researcher conclude that the drug is effective? Use the P - value method

Medication Effective Not effective

Drug 32 9

Placebo 12 18

I need help with these 2 problems as well and I need it to include

a. State the hypotheses and identify the claim

b. Find the critical value

c. Compute the test value

d. Make the decision

e. Summarize the results

Question# 5.Combating Midday Drowsiness. A researcher wishes to see if the five ways (drinking decaffeinated beverages, taking a nap, going for a walk, eating a sugary snack, other) people use to combat midday drowsiness are equally distributed among office workers. A sample of 60 office workers is selected, and the following data are obtained. At a = 0.10 can it be concluded that there is no preference? Why would the results be of interest to an employee?

Method Beverage Nap Walk Snack Other

Number 21 16 10 8 5

Question 6. On-Time Performance by airlines. According to the Bureau of Transportation statistics, on-time performance by airlines is described as follows:

Action % of time

On time 70.8

National Aviation System Delay 8.2

Aircraft arriving late 9.0

Other (because of weather and other conditions) 12.0

Records of the 200 flights for a major airline company showed that 125 planes were on time, 40 were delayed because of weather, 10 because of a national aviation system delay and the rest because of arriving late. At a = 0.05 do these results differ from the government's statistics?

#### Solution Preview

I need help with the following 4problems and they need to include

a. State the hypotheses and identify the claim

b. Find the critical value

c. Compute the test value

d. Make the decision

e. summarize the results and explain where the differences in the mean are

Question # 1 Number of State Parks The number of state parks found in selected states in three different regions of the country are listed below at a = 0.05 can it be concluded that the average number of state parks differ by region

South West New England

51 28 94

64 44 72

35 24 14

24 31 52

47 40

Solution:

Claim: To find whether the average number of state parks differ by region.

Hypotheses:

H0: µ1 = µ2 = µ3

H1: µ1 ≠ µ2 ≠ µ3

Critical value:

F0.05, 2, 11 = 3.98

Test Statistic:

By Using Excel

One factor ANOVA

Mean n Std. Dev

44.2 5 15.32 South

33.4 5 8.35 West

58.0 4 33.98 New England

44.3 14 21.53 Total

ANOVA table

Source SS df MS F p-value

Treatment 1,344.86 2 672.429 1.58 .2494

Error 4,682.00 11 425.636

Total 6,026.86 13

Decision:

Since the f calculated value(1.58) is less than the critical value(3.98) we may accept the null hypotheses

Conclusion:

Hence we conclude that average number of state parks does not differ by region

Question # 2 Grams of fat per serving of pizza. The number of grams of fat per serving for three different kinds of pizza from several manufacturers is listed below. At the 0.01 level of significance, is there sufficient evidence that a difference exists in the mean fat content?

Cheese Pepperoni Supreme/Deluxe

18 20 16

11 17 27

19 15 17

20 18 17

16 23 12

21 23 27

16 21 20

Solution:

Claim: To find whether difference exists in the mean fat content.

Hypotheses:

H0: µ1 = µ2 = µ3

H1: µ1 ≠ µ2 ≠ µ3

Critical value:

F0.05, 2, 18 = 6.01

Test Statistic:

By Using Excel

One factor ANOVA

Mean n Std. Dev

17.3 7 3.35 Cheese

19.6 7 3.05 Pepperoni

19.4 7 5.68 Supreme

18.8 21 4.12 Total

ANOVA table

Source SS df MS F p-value

Treatment 22.95 2 11.476 0.65 .5329

Error 316.86 18 17.603

Total 339.81 20

Decision:

Since the f calculated value(0.65) is less than the critical value(6.01) we may accept the null hypotheses

Conclusion:

Hence we conclude ...

#### Solution Summary

The solution examines hypothesis tests and identifies the claim. The critical and test value are determined for multiple situations.