Q1) "Wheat" pennies are pennies which are minted before 1954. Following data represent weight (in grams) of random sample of 15 wheat pennies.
|
3.01
|
3.06
|
3.13
|
3.00
|
3.05
|
|
3.07
|
3.02
|
2.98
|
3.04
|
3.02
|
|
3.06
|
3.03
|
3.07
|
3.04
|
2.96
|
i) What is the point estimate?
ii) What is the standard deviation?
iii) Construct a 90% confidence interval for the mean weight of a "wheat" penny.
iv) What could be done to increase the accuracy of the interval without changing the level of significance?
v) Find the t-value such that the area in the right tail is .10 with 25 degrees of freedom
vi) Find the t-value such that the area in the right tail is 0.05 with 30 degrees of freedom.
vii) Find the t-value such that the area left of the t-value is 0.01 with 18 degrees of freedom
viii) Find the critical t-value that corresponds to 90% confidence. Assume 90 degrees of freedom.
ix) What are 4 properties of the t-distribution?