Question

In: Statistics and Probability

A random sample of size n = 130 is taken from a population with a population...

A random sample of size n = 130 is taken from a population with a population proportion p = 0.58. (You may find it useful to reference the z table.)

a. Calculate the expected value and the standard error for the sampling distribution of the sample proportion. (Round "expected value" to 2 decimal places and "standard error" to 4 decimal places.)

b. What is the probability that the sample proportion is between 0.50 and 0.70? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

c. What is the probability that the sample proportion is less than 0.50? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

Solutions

Expert Solution

Solution:

Given that,

n = 130

= 0.58

1 - = 1 - 0.58 = 093

a )   =   = 0.542

= ( 1 - ) / n

=   0.58* 0.42 / 130

= 0.0433

= 0.0433

P( 0.50 < < 0.70 )  

b )P( 0.50 - 0.58 / 0.0433 ) < ( -    / ) < ( 0.70 - 0.58 / 0.0433 )

P ( - 0.08 /0.0433< z < 0.12 / 0.0433)

P ( - 1.85 < z < 2.77 )

P ( z < 2.77 ) - p ( z < -1.85 )

Using z table

= 0.9972 - 0.0322

= 0.9650

Probability = 0.9650

c ) P (   < 0.50 )

P ( -    / ) < ( 0.50 - 0.58 / 0.0433 )

P ( z < - 0.08 / 0.0433 )

Using z table

P ( z < -1.85 )

=0.0322

Probability = 0.0322


Related Solutions

A random sample of size n = 100 is taken from a population of size N...
A random sample of size n = 100 is taken from a population of size N = 600 with a population proportion of p =0.46. Is it necessary to apply the finite population correction factor? Calculate the expected value and standard error of the sample proportion. What is the probability that the sample mean is less than .40?
A random sample of size n = 69 is taken from a population of size N...
A random sample of size n = 69 is taken from a population of size N = 971 with a population proportion p = 0.68. a-1. Is it necessary to apply the finite population correction factor? Yes or no? a-2. Calculate the expected value and the standard error of the sample proportion. (Round "expected value" to 2 decimal places and "standard error" to 4 decimal places.) Expected Value- Standard Error- b. What is the probability that the sample proportion is...
A random sample of size n = 71 is taken from a population of size N...
A random sample of size n = 71 is taken from a population of size N = 639 with a population proportion p = 0.73. a-1. Is it necessary to apply the finite population correction factor? a-2. Calculate the expected value and the standard error of the sample proportion. (Round "expected value" to 2 decimal places and "standard error" to 4 decimal places.) b. What is the probability that the sample proportion is less than 0.66? (Round “z” value to...
A random sample of size n = 152 is taken from a population of size N...
A random sample of size n = 152 is taken from a population of size N = 3,300 with mean μ = −71 and variance σ2 = 112. [You may find it useful to reference the z table.] a-1. Is it necessary to apply the finite population correction factor? Yes No a-2. Calculate the expected value and the standard error of the sample mean. (Negative values should be indicated by a minus sign. Round "standard error" to 2 decimal places.)...
A random sample of size n = 472 is taken from a population of size N...
A random sample of size n = 472 is taken from a population of size N = 9,700 with mean μ = −63 and variance σ2 = 176. [You may find it useful to reference the z table.] A-1 Is it necessary to apply the finite population correction factor? Yes No a-2. Calculate the expected value and the standard error of the sample mean. (Negative values should be indicated by a minus sign. Round "standard error" to 2 decimal places.)...
A random sample of size n = 225 is taken from a population with a population...
A random sample of size n = 225 is taken from a population with a population proportion P = 0.55. [You may find it useful to reference the z table.] a. Calculate the expected value and the standard error for the sampling distribution of the sample proportion. (Round "expected value" to 2 decimal places and "standard error" to 4 decimal places.) b. What is the probability that the sample proportion is between 0.50 and 0.60? (Round “z” value to 2...
A random sample of size n is taken from a normally distributed population with a population...
A random sample of size n is taken from a normally distributed population with a population standard deviation (σ ) of 11.6. The sample mean (x) is 44.6. Construct a 99% confidence interval about µ with a sample size of 26.
A random sample of size n = 55 is taken from a population with mean μ...
A random sample of size n = 55 is taken from a population with mean μ = −10.5 and standard deviation σ = 2. [You may find it useful to reference the z table.] a. Calculate the expected value and the standard error for the sampling distribution of the sample mean. (Negative values should be indicated by a minus sign. Round "expected value" to 1 decimal place and "standard error" to 4 decimal places.) b. What is the probability that...
A random sample of size n = 50 is taken from a population with mean μ...
A random sample of size n = 50 is taken from a population with mean μ = −9.5 and standard deviation σ = 2. [You may find it useful to reference the z table.] a. Calculate the expected value and the standard error for the sampling distribution of the sample mean. (Negative values should be indicated by a minus sign. Round "expected value" to 1 decimal place and "standard deviation" to 4 decimal places.) Expected Value= Standard Error= b. What...
1. A random sample of size n = 10 is taken from a large population. Let...
1. A random sample of size n = 10 is taken from a large population. Let μ be the unknown population mean. A test is planned of H0: μ=12vs. HA: μ̸=12usingα=0.1. A QQ plot indicates it is reasonable to assume a normal population. From the sample, x̄ = 14.2 and s = 4.88. (I suggest doing this problem with a calculator and table as practice for exams. You may check your answers with R if you wish.) (a) Since the...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT