1 The normal distribution can be used to approximate the sam

1) The normal distribution can be used to approximate the sampling distribution of the sample proportion with a probability of success .77, if the sample size is greater than or equal to

2) The standard error of the mean for a smale size of 153 is 25. In order to cut the standard error of the mean in half(to 12.5) we must select a sample size of?

3) An infinite population has a mean of 73 and a standard deviation of 38. A sample size of 121 is taken at random from this population. The standard error of the sample mean equals:

Please show all steps. Thank you

Solution

np >5 and n(1-p) > 5 for normal approximation

p=0.77

np>5      n*0.77 >5    n> 5/0.77 =6.49

rounded to next number 7

n(1-0.77) >5      n >5/0.23 =21.7

rounded to next number = (maximum of 7,22) = 22

The required sample size =22

2) The standard error of the mean for a sample size of 153 is 25. In order to cut the standard error of the mean in half(to 12.5) we must select a sample size of?

standard error of the sample mean = se = sd/sqrt(n)

to reduce se by half,   se/2=sd/(2*sqrt(153)) =sd/sqrt(4*153)

we have to take 4 times of the sample size = 4*153=612

the required sample size =612

3) An infinite population has a mean of 73 and a standard deviation of 38. A sample size of 121 is taken at random from this population. The standard error of the sample mean equals:

standard error of the sample mean = sd/sqrt(n) = 38/sqrt(121) =3.4545