Question

1. A recent survey of students asked about the use of marijuana. Of the 600 women sampled, 450 responded that they chose to notuse marijuana.

The proportion of women not using marijuana is ______.____ %2.

The margin of error (95%) of this estimate is ______.____ %3.

The 95% confidence interval for the proportion is from ______.____ % to ______.____ %

Sarah believes that 60% of women students choose to not use marijuana. Select and complete one of the following statements using the confidence interval calculated above.I reject Sarah’s hypothesis because __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

I cannot reject Sarah’s hypothesis because _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Answer 1

sample proportion, = 0.75
sample size, n = 600
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.75 * (1 - 0.75)/600) = 0.0177

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

Margin of Error, ME = zc * SE
ME = 1.96 * 0.0177
ME = 0.03469

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.75 - 1.96 * 0.0177 , 0.75 + 1.96 * 0.0177)
CI = (0.7153 , 0.7847)

The proportion of women not using marijuana is 75%

The margin of error (95%) of this estimate is 3.469%.

The 95% confidence interval for the proportion is from 71.5308 % to 78.4692 %

I reject Sarah’s hypothesis because confidence interval does not contain hypothesised value which is 60%

answered by: anonymous