A researcher wants to estimate the proportion of a populatio

A researcher wants to estimate the proportion of a population which possesses a given characteristic A random sample of size 200 is taken and 30% of the sample possesses the characteristic The 95% confidence interval to estimate the population proportion is Suppose you are testing the null hypothesis that a population mean is 80. The sample is 49 and alpha =.05. If the sample mean is 84 and the population standard deviatio14, the observed (calculated) z value is.

Solution

14) Std. error = ( 0.3 * 0.7 / 200) and z-score for 95% confidence = 1.96.. sample proportion = 0.3...
Confidence interval = [ sample mean - ( z-score * standard error) , sample mean+( z*score * std. error) ]

95% confidence interval for population proportion is

= [ 0.3 - ( 1.96 * sqrt ( 0.3 * 0.7 / 200 ) ) ,  0.3 + ( 1.96 * sqrt ( 0.3 * 0.7 / 200 ) ) ]

= [ 0.24 , 0.36 ] ( c)

15) z- value = ( sample mean - population mean) / ( population s.d / sqrt ( sample size ) )
= [ 84 - 80 / ( 14 / sqrt ( 49 ) ] = 2...(a)