What is a 95 percent confidence interval for type I of tumor? (Use Xbar +/- t(n-1)alpha/2 ( T value from T table) * S / square root of n)

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ANSWER ALL QUESTIONS

Question 1) The following is a tumor size for two different types of breast cancer.

(each part 2.5-point total 10 points) 

Type of tumor	n		s
I	20	3.5	1.80
II	15	2.7	1.50

a) What is a 95 percent confidence interval for type I of tumor? (Use Xbar +/- t(n-1)alpha/2 ( T value from T table) * S / square root of n)

1. 2.66 and 4.34

2. 4.50 and 5.67

3. 3.5 and 6.39

4. 1.87 and 3.53

b) What is a 95 percent Confidence interval for type II of tumor? (Use Xbar +/- t(n-1),1-alpha/2 ( T value from T table) * S / square root of n)

c)

1. 2.66 and 4.34

2. 4.50 and 5.67

3. 3.5 and 6.39

4. 1.87 and 3.53

c) Is the following interpretation for part a and b are true or false: The results indicate that we have 95% confidence that the true mean of tumor size for type I and Type II are (2.66, 4.34) and (1.87,3.53); Respectively.

1. True

2. False

d) What is a 99 percent confidence interval for the difference between populations mean? (First find S pooled by using S2p= (n1-1) * S21 + (n2-1) * S22/ n1 +n2 -2 then use xbar1-xbar2 +/- T ( n1+n2-2,1-alpha/2 ( t value from T table) * square root of (s2p/n1 + s2p/n2))

5. .66 and 4.34

6. .50 and 3.67

7. -.76 and 2.36

8. -1.87 and 5.53

Question 2) In a survey to identify of risk factors for heart disease among men and women were asked about if they ever smoke. Of the 430 men, 116 said they smoke. Of the 380 women, 73 said they smoke. (Each parts 2 points for total 12 points)

a) What is the proportion for smoker for men? (Use P = x/n)

1. .30

2. .27

3. .50

4. .20

b) What is the proportion for smoker for women? (Use P = x/n)

1. .30

2. .27

3. .50

4. .19

 

 

c) What is a 95 percent confidence interval for the proportion smoker for men? (Use p +/- Z 1-alpha/2 ( find Z value from Z table) * square root of P* (1-.p)/ n. Use P .2698 four digit to get exact value. Otherwise, yours would be a little off)

1. .23 and .31

2. .37 and .45

3. .15 and .23

4. .10 and .30

d) What is a 95 percent confidence interval for the proportion smoker for women? (Use p +/- Z 1-alpha/2 ( find Z value from Z table) * square root of P* (1-.p)/ n. Use P .1921 four digit to get exact value. Otherwise, yours would be a little off)

e)

1. .23 and .31

2. .37 and .45

3. .15 and .23

4. .10 and .30

e) Is the following interpretation for part c and d are true or false: We have 95 percent confidence that the true proportions of smoker for men is between .226 and .3136. Also, there is 95 % confidence that the true proportion of smoker for women is between .153 and .231.

1. False

2. True

f) f) What is a 90 percent confidence interval for the difference between the proportion populations for smoker? (Use p1 – p2 +/- Z 1-alpha/2 ( find Z value from Z table) * square root of P1* (1-.p1)/ n1 + P2 * (1-P2)/n2). Use P1= .2698 and P2 =.1921 four digit to get exact value. Otherwise, yours would be a little off)

 

1. .03 and .13

2. .10 and .40

3. .20 and .43

4. .05 and .50

 

Question3) Let say a researcher who studied on a chronic disease hospital outpatient. The following are the information researcher find from 49 records. The average outpatient visits per patients was 6 and the population standard of deviation of 3. ((each part 3 point total 9 point )

 

a) What statistical test researcher should use?

1. One proportion test

2. One sample Z-test when population variance is unknown

3. One sample Z-test when population variance is known

4. None of above

b) If researcher want to conclude that the population mean is greater than 5 visits per patients what is the value of Z statistics? (Use Z= xbar – Mu/ sigma / square root of n)

1. 5.6

2. 2.33

3. -3.5

4. -4.5

c) Can a researcher conclude that the population mean is greater than 5 visits per patients? Let alpha be at .05.

1. Yes, because our test statistics is greater than Z value from Z table

2. No, because our test statistics is less than Z value from Z table

 

Question4) Let say a researcher who studied on daily caloric intake for certain adult population. A research take a sample of 36 had the mean of 1900 with the sample standard deviation of 100. (Each parts 3 points for total of 9 points)

a) What statistical test researcher should use?

1. One proportion test

2. One sample T-test when population variance is unknown

3. One sample T-test when population variance is known

4. None of above

b) If researcher want to conclude that the population mean of caloric intake is greater than 1801 what is the value of T statistics? (Use t= xbar – Mu/ S / square root of n)

 

1. 5.97

2. 2.33

3. -3.5

4. -4.5

c) Can a researcher conclude that the population mean of caloric intake is greater than 1801? Let alpha be at .01

1. Yes, because our test statistics is greater than T value from T table

2. No, because our test statistics is less than T value from T table

Question 5) The following is a physical activity score for two groups in study. The higher score means the more physical activity

(Part a and b 3 points and part c and d 1.5 point) 

Group	n		s
Control	100	40	8
Intervention	100	50	10

a) What statistical test researcher should use?

1. Two sample T-test when population variance is known

2. One sample T-test when population variance is unknown

3. One sample T-test when population variance is known

4. Two samples T-test when population Variance is unknown

 

b) What is the Pooled variance for these two groups? (Use S pooled by using S2p= (n1-1) * S21 + (n2-1) * S22/ n1 +n2 -2)

1. 82

2. 2.80

3. 1.50

4. 2.00

 

d) c) What is the value of T statistics? (use xbar1-xbar2 – 0 divided by square root of (s2p/n1 + s2p/n1))

 

1. -5.60

2. -3.00

3. 5.60

4. -7.81

d) Can we conclude the mean of physical activity is different for intervention as compare to control at alpha .01?

1. Yes, because our absolute test statistics is greater than T value from T table

2. No, because our absolute test statistics is less than T value from T table

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