The following questions regard t distributions. Using the t-distribution table,
ID: 3135097 • Letter: T
Question
The following questions regard t distributions. Using the t-distribution table, find the 95th percentile of t(11) denoted by t_o.05(H) and the 5th percentile of t(11). Find the interval containing the middle 90% of values of t distribution with 11 degrees of freedom and use your answer to provide the 90% confidence interval formula for population mean meu based on a sample of size 12 with sample standard deviation S. How does the 90% confidence interval formula in part (b) change if the sample size increases to 24? How does the confidence interval formula in part (b) change if the confidence level increases to 95% with the same sample size of 12? The one-sample t statistic for testing H_0 : MEU = 10 versus H_a : meu > 10 from a sample of n = 18 observations has the value t = 2.05. What are the degrees of freedom for this statistic? Give the two critical values from the t-distribution table that bracket t and express the two values using the notation t_alpha(k) with appropriate alpha and k. Between what two values does the P-value of the test fall? Is the value t = 2.05 significant at the 5% level? Is it significant at the 1% level? Using R, find the exact P-value of t = 2.05.Explanation / Answer
a)95% for 11dof=1.796, t(0.05)=-1.796
b)CI=[u-1.796S,u+1.796S]
For mean---->[u-1.796S/sqrt(12),u+1.796S/sqrt(12)]
c)n=24, t(0.95)=1.714
CI=[u-1.714S,u+1.714S]
For mean--->[u-1.714S/sqrt(24),u+1.714S/sqrt(24)]
d)95% CI,n=12, t=2.201
CI=[u-2.201S,u+2.201S]
For mean---->[u-2.201S/sqrt(12),u+2.201S/sqrt(12)]
e)dof=17
talpha/2(17),-talpha/2(k)
t(0.025,17)=2.11 t(0.005,17)=2.898
as t<tcritical in both the cases,it is not significant.
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