For this problem, carry at least four digits after the decimal in your calculati
ID: 3264049 • Letter: F
Question
For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. The National Council of Small Businesses is interested in the proportion of small businesses that declared Chapter 11 bankruptcy last year. Since intends to estimate the proportion from a random sample. Let p be the proportion of small businesses t of small businesses that declared Chapter 11 bankruptcy last year. Since there are so many small businesses, the National Couna hat declared Chapter 11 bankruptcy last year 95% sure that a point estimate p will be within a distance of 0.12 from p? (Round your answer up to taken to estimate P. how large a sample is necessary to be (a) if no preliminary sample the nearest whole number.) 67 sinall businesses (b) In a preliminary random sample of 30 small businesses, t was 95% sure that a point estimate P will be within a distance 95 random sample of 30 small businesses, i was found that seven had declared Chepter 11 bankruptcy. How many more small businesses should be included in the sample to be estimate p will be within a distance of 0.120 from p? (Round your answer up to the nearest whole number.) more small businesses XExplanation / Answer
Answer:
Problem1).
b. for sample p=0.2333, estimated sample size=
Sample size = (z2*p*(1-p))/d2
= (1.962*0.2333*0.7667)/0.1202
=47.7
The sample size required= 48
Answer: 18 more small businesses
Problem 2
Test statistic z = 3.29
P=0.0010
Z Test of Hypothesis for the Mean
Data
Null Hypothesis m=
28
Level of Significance
0.01
Population Standard Deviation
4.75
Sample Size
7
Sample Mean
33.9
Intermediate Calculations
Standard Error of the Mean
1.7953
Z Test Statistic
3.2863
Two-Tail Test
Lower Critical Value
-2.5758
Upper Critical Value
2.5758
p-Value
0.0010
Reject the null hypothesis
Problem 3
Test statistic z=0.88
P=0.1892
Z Test of Hypothesis for the Mean
Data
Null Hypothesis m=
4.6
Level of Significance
0.01
Population Standard Deviation
2.8
Sample Size
10
Sample Mean
5.38
Intermediate Calculations
Standard Error of the Mean
0.8854
Z Test Statistic
0.8809
Upper-Tail Test
Upper Critical Value
2.3263
p-Value
0.1892
Do not reject the null hypothesis
Z Test of Hypothesis for the Mean
Data
Null Hypothesis m=
28
Level of Significance
0.01
Population Standard Deviation
4.75
Sample Size
7
Sample Mean
33.9
Intermediate Calculations
Standard Error of the Mean
1.7953
Z Test Statistic
3.2863
Two-Tail Test
Lower Critical Value
-2.5758
Upper Critical Value
2.5758
p-Value
0.0010
Reject the null hypothesis
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