Question

In: Statistics and Probability

A sample of 150 was obtained of men with each of three types of cancer, and...

A sample of 150 was obtained of men with each of three types of cancer, and the following data show blood types for each. Use an appropriate test, determine if blood type of cancer type are related. (Contingency table )

Blood Type

Cancer Type

O

A

B

AB

Colon

61

65

18

6

Lung

69

57

15

9

Prostate

73

60

12

5

Solutions

Expert Solution

Claim: blood type of cancer type are related.

The null and alternative hypothesis is

H0: blood type of cancer type are not related.

H1: blood type of cancer type are related.

Level of significance = 0.05

Test statistic is

O: Observed frequency
E: Expected frequency.
E = ( Row total*Column total) / Grand total

Blood Type
Cancer Type O A B AB Total
Colon 61 65 18 6 150
Lung 69 57 15 9 150
Prostate 73 60 12 5 150
Total 203 182 45 20 450
O E (O-E) (O-E)^2 (O-E)^2/E
61 67.66667 -6.66667 44.44444 0.656814
65 60.66667 4.333333 18.77778 0.309524
18 15 3 9 0.6
6 6.666667 -0.66667 0.444444 0.066667
69 67.66667 1.333333 1.777778 0.026273
57 60.66667 -3.66667 13.44444 0.221612
15 15 0 0 0
9 6.666667 2.333333 5.444444 0.816667
73 67.66667 5.333333 28.44444 0.420361
60 60.66667 -0.66667 0.444444 0.007326
12 15 -3 9 0.6
5 6.666667 -1.66667 2.777778 0.416667
Total 4.14

Degrees of freedom = ( Number of rows - 1 ) * ( Number of column - 1) = ( 3 - 1) * (4 - 1) = 2 * 3 = 6
Critical value = 12.592

( From chi-square table)

Test statistic < critical value we fail to reject the null hypothesis.

Conclusion:

Blood type of cancer type are not related.


Related Solutions

A random sample of 150 men found that 88 of the men exercise regularly, while a...
A random sample of 150 men found that 88 of the men exercise regularly, while a random sample of 200 women found that 130 of the women exercise regularly. a. Based on the results, construct and interpret a 95% confidence interval for the difference in the proportions of women and men who exercise regularly. b. A friend says that she believes that a higher proportion of women than men exercise regularly. Does your confidence interval support this conclusion? Explain.
A) List three types of skin cancer. Describe the likely risk factors for each and the...
A) List three types of skin cancer. Describe the likely risk factors for each and the prognosis and treatment for each. B) Which skin cancer has the highest mortality rate and why? How would you make the diagnose of this disease?
How is a random sample obtained? Name two types of target populations, briefly describe each. What...
How is a random sample obtained? Name two types of target populations, briefly describe each. What implications would arise from a low response rate on a survey?
A simple random sample of men who regularly work out at Mitch's Gym is obtained and...
A simple random sample of men who regularly work out at Mitch's Gym is obtained and their resting pulse rates (in beats per minute) are listed below. 54 60 67 84 74 64 69 70 66 80 59 71 76 63 Use a 0.05 significance level to test the claim that the mean resting pulse rates is less than 72 beats per minute. Assume that the resting pulse rates of all men who work out at Mitch's Gym are normally...
Assume that each sample is a simple random sample obtained from a population with a normal...
Assume that each sample is a simple random sample obtained from a population with a normal distribution. a. n= 93 mean=3.90968 s=0.51774 Construct a 99​% confidence interval estimate of the standard deviation of the population from which the sample was obtained. b. n=93 mean=4.09355 s=0.59194 Repeat part​ (a). How do you find values on a chi-square table when the degrees of freedom are a value not commonly found on standard chi-square tables? (In this case, 92)
We had n=150 and σ=6.2, use the added information that the efficiency experts obtained the sample...
We had n=150 and σ=6.2, use the added information that the efficiency experts obtained the sample mean (x̅=69.5) to calculate a 95% confidence interval for the average mechanical aptitude of assembly line workers in the given industry.
Lung cancer is the second most common cancer among men and women in the USA. You...
Lung cancer is the second most common cancer among men and women in the USA. You are hired as a manager-planner by one of the hospitals. The organization is interested in establishing a community outreach program promoting smoking cessation and lung cancer screening. The Board of Directors requested your services in processing the data collected through the prospective cohort study among male and female population visiting local gym. The data set is attached. Please use Excel or Epi Info to...
If p = 0.05 and the sample size of each subgroup is 150, then calculate the...
If p = 0.05 and the sample size of each subgroup is 150, then calculate the control limits for: a) p chart b) np chart
IN 150 WORDS OR MORE Identify data types. When are each useful?
IN 150 WORDS OR MORE Identify data types. When are each useful?
The foot size of each of 16 men was measured, resulting in the sample mean of...
The foot size of each of 16 men was measured, resulting in the sample mean of 27.32 cm. Assume that the distribution of foot sizes is normal with sigma = 1.2 cm. a) Test if the population mean of men’s foot sizes is 28.0 cm using alpha = 0.01. b) If alpha = 0.01 is used, what is the probability of a type II error when the population mean is 27.0 cm? c) Find the sample size required to ensure...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT