If the true mean is really 38, we are almost certain to reject the false null hypothesis.
For a given margin of error using P * = 0.5:
To reduce the margin of error by a factor of 0.5, we haveWe need to quadruple the sample size to reduce the margin of error by a factor of 1 / 2 .Hence,The department should ask at least 35 students about their intentions.
The finding is statistically significant because the P -value is less than the significance level. In this
situation, it is unlikely that we would have obtained a value of 1 – 2 = 0. as different from 0 as we
got by chance alone if, in fact, 1 – 2 = 0.
- Trick question! The sample size needed for a 95% confidence interval (or any C -level interval for
that matter) is not a function of population size. The sample size needed is given by
n is a function of z * (which is determined by the confidence level), M (the desired margin of error),
and P * (the estimated value of ). The only requirement is that the population size be at least 20
times as large as the sample size.
Because n = 50, we could use a large-sample confidence interval. For n = 50, z * = 2.33 (that’s the
upper critical z -value if we put 1% in each tail).
Anna tells her father that he can be 98% confident that the true average test score for his 41 years of
teaching is between 71.16 and 75.84.