Question

11. A random sample of 25 statistics examinations was taken. The average score in the sample was 76 with a variance of 144. Assuming the scores are normally distributed, the 99% confidence interval for the population average examination score is 70.02 to 81.98 6. 69.82 to 82.18 70.06 to 81.94 d. 69.48 to 82.52 2. c. 12. It is known that the population variance equals 484. With a 0.95 probability, the sample size that needs to be taken to estimate the population mean if the desired margin of error is 5 or less is 25 b. 74 189 d. 75 13. For the interval estimation of u when o is assumed known, the proper distribution to use is the standard normal distribution b. 1 distribution with a degrees of freedom c. 1 distribution with n - 1 degrees of freedom d. 1 distribution with - 2 degrees of freedom 14. A Type I error is committed when a true alternative hypothesis is not accepted b. a true null hypothesis is rejected the critical value is greater than the value of the test statistic d. sample data contradict the null hypothesis

Answer 1

11.

here n = 25

xbar = 76, s^2 = 144 , s= 12

c-level = 99%=0.99

so t critical value with degrees of freedom = n-1 = 25-1 =24 and for confidence level 0.99 so significance level = 1-c-level = 1-0.99=0.01 is,

calculated using below command

=TINV(0.01,24)

=2.797

So t crit = 2.797

99% confidence interval for mean is

xbar - (t crit * s/ root(n)) and xbar + (t crit * s/root(n))

76 - (2.797 * 12/root(25)) and 76 + (2.797 * 12/root(25))

76 - (2.797 * 12/5 ) and 76 + (2.797 * 12/5 )

76 - (2.797 * 2.4) and 76 + (2.797 * 2.4)

76 - 6.7128 and  76 + 6.7128

69.2872 and 82.7128

69.29,82.71

which is very close to option d) 69.48,82.52

So option d) is correct

12.

Here variance (sigma^2)=484 so sigma = 22

margin of error = E = 5

z for 0.95 or c-level = 95% using probability below z is (1+clevel)/2 = (1+0.95)/2=0.975

and excel command

=NORMSINV(0.975)

=1.96

so n = (z*sigma)^2/E^2 = (1.96*22)^2/5^2 = 43.12^2 /25=1859.334/25=74.373

rounded n to next nearest integer we get n = 75

So answer is option d) 75 is correct

13.

We use standard normal distribution when population standard deviation is known to estimate interval

So option a) Standard Normal Distribiution is correct

14.

A type 1 error is reject H0 when H0 is true

So option b) A true null hypothesis is rejected. is correct