Question

In: Statistics and Probability

A simple random sample of 600 elements generates a sample proportion P=0.60    a. Provide the 90%...

A simple random sample of 600 elements generates a sample proportion P=0.60   

a. Provide the 90% confidence interval for the population proportion (to 4 decimals).

b. Provide the 95% confidence interval for the population proportion (to 4 decimals).

Solutions

Expert Solution

Solution :

Given that,

n = 600

Point estimate = sample proportion = = = 0.60

1 -   = 1- 0.60 =0.40

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

Margin of error = E Z/2 *(( * (1 - )) / n)

= 1.645 *((0.60*0.40) /600 )

= 0.0329

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.60-0.0329 < p <0.60+ 0.0329

0.5671< p < 0.6329

The 90% confidence interval for the population proportion p is : 0.5671, 0.6329

(B)

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E = Z/2   * ((( * (1 - )) / n)

= 1.96 *((0.60*0.40) /600 )

= 0.0392

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.60-0.0392< p < 0.60+0.0392

0.5608< p < 0.6392

The 95% confidence interval for the population proportion p is : 0.5608, 0.6392


Related Solutions

A simple random sample of 800 elements generates a sample proportion of 0.70. Provide a 90%...
A simple random sample of 800 elements generates a sample proportion of 0.70. Provide a 90% confidence interval for the population proportion. (round to two decimal places) [Answer , Answer] Provide a 99% confidence interval for the population proportion. (round to two decimal places) [Answer , Answer]
A simple random sample of 1000 elements generates a sample proportion p =0.68   a. Provide the...
A simple random sample of 1000 elements generates a sample proportion p =0.68   a. Provide the confidence interval for the population proportion (to 4 decimals). , (     , ) b. Provide the confidence interval for the population proportion (to 4 decimals). , ( , )
A simple random sample of 500 elements generates a sample proportion p = 0.72  a. Provide...
A simple random sample of 500 elements generates a sample proportion p = 0.72  a. Provide the 99% confidence interval for the population proportion (to 4 decimals). (    , ) b. Provide the 90% confidence interval for the population proportion (to 4 decimals). ( , )
4. A simple random sample of 800 elements generates a sample proportion j5 = .70. a....
4. A simple random sample of 800 elements generates a sample proportion j5 = .70. a. Provide a 90% confidence interval for the population proportion. b. Provide a 95% confidence interval for the population proportion.
The population proportion is 0.60. What is the probability that a sample proportion will be within...
The population proportion is 0.60. What is the probability that a sample proportion will be within ±0.04 of the population proportion for each of the following sample sizes? Round your answers to 4 decimal places. Use z-table. A.) n=100 B.) n= 200 C.) n=500 D.) n=1,000
A population proportion is 0.60. Suppose a random sample of 660 items is sampled randomly from...
A population proportion is 0.60. Suppose a random sample of 660 items is sampled randomly from this population. Appendix A Statistical Tables a. What is the probability that the sample proportion is greater than 0.62? b. What is the probability that the sample proportion is between 0.56 and 0.62? c. What is the probability that the sample proportion is greater than 0.59? d. What is the probability that the sample proportion is between 0.58 and 0.59? e. What is the...
Find the 10 th and the 90 th percentiles of sample proportion ^ p , if...
Find the 10 th and the 90 th percentiles of sample proportion ^ p , if the population proportion p = 0.15 and the sample size n = 125.
A) Assume that a sample is used to estimate a population proportion p. Find the 90%...
A) Assume that a sample is used to estimate a population proportion p. Find the 90% confidence interval for a sample of size 246 with 64% successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places. C.I. = B) Assume that a sample is used to estimate a population proportion p. Find the 95% confidence interval for a sample of size 160 with 62% successes. Enter your answer as an open-interval (i.e.,...
A simple random sample of 60 items resulted in a sample mean of 90. The population...
A simple random sample of 60 items resulted in a sample mean of 90. The population standard deviation is 12. a. Compute the 95% confidence interval for the population mean (to 1 decimal). ( ? , ? ) b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean (to 2 decimals). ( ? , ? )
A simple random sample of 90 items from a population with  = 9 resulted in a sample...
A simple random sample of 90 items from a population with  = 9 resulted in a sample mean of 36. If required, round your answers to two decimal places. a. Provide a 90% confidence interval for the population mean.   to   b. Provide a 95% confidence interval for the population mean.   to   c. Provide a 99% confidence interval for the population mean.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT