Question

True or False

6. T F n= 60 is used to separate the use of normal and t distributions in calculating confidence intervals for populations with unknown variances.

7. T F Decreasing α will shorten a confidence interval.

8. T F The chi square distribution is used to establish confidence intervals for variances.

9. T F At n= 20 and probability = .95, the t value is larger than the z value.

10. T F For the same α, the t statistic is smaller than the z statistic.

Answer 1

6. False

because if n is less than 30 we use t distribution for calculating confidence interval and if n is more than 30 we use normal distribution but not particularly n=60

7.False

Decreasing a (alpha) will result in increasing confidence level, because a(alpha) = 1-confidence level

so increase in confidence level will increse confidence interval as we know

8.True

because, distrbution of sample variances is Chi-Sq. Always

9.True

we can check this manually by calculating critical values

10.False

t statistic and z statistic does not depend on a(alpha)

it only depends on value of sample mean, sample size and standard deviation