The t-distribution must be used when the sample size is greater than 30 and the

Question

The t-distribution must be used when the sample size is greater than 30 and the variable is normally or approximately normally distributed A. true B. False QUESTION 1 2 points Save Answer 12 squirrels were found to have an average weight of 10.5 ounces with a sample standard deviation is 0.25. Find the 95% confidence interval of the true mean weight. O (9.75, 11.25) O (0.31, 10.69) QUESTION 2 2 points Save Answer In a study of size 9 where the variance is unknown, the distribution that should be used to calculate confidence intervals is O a normal distribution O a t distribution with 8 degrees of freedom O at distribution with 9 degrees of freedom O at distribution with 10 degrees of freedom QUESTION 3 2 points The winning team's scores in 13 high school basketball games were recorded. If the sample mean is 10.4 points and the sample standard deviation is 0.15 points, find the 98% confidence interval of the true mean O (10.36, 10.44) (10.29, 10.51) O 10.30, 10.50) A 4 129 AM 4/8/2017

Explanation / Answer

1.Answer: First option is correct

N= 12, mean = 10.5, S =0.25

Mean ± t(alpha/2)),N-1 (S/sqrt(N))

As 95% confidence interval is asked to compute hence alpha = 0.05

t(alpha/2)),N-1 = t0025,11 = 2.20

S/sqrt(N)= 0.25/sqrt(12) = 0.072

Lower limit = 10.5 – (2.20* 0.072 ) = 10.34

Upper Limit = 10.5 + (2.20*

2.Answer: Second Option

When variance is unknown then t-distribution is recommended and degrees freedom is n-1. Here n (number of observations are 9) hence degrees of freedom is 8.

3.Answer to (5) is False.

t-distribution is recommended in case where sample size is small (which is less than 30)

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