Question

1) A random sample of 10 observations was drawn from a large normally distributed population. The data is below.

23,19, 24,17, 19, 23, 22, 22, 17, 16,

Test to determine if we can infer at the 8% significance level that the population mean is not equal to 20, filling in the requested information below.

A. The value of the standardized test statistic:

Note: For the next part, your answer should use interval notation. An answer of the form (−∞,?)  is expressed (-infty, a), an answer of the form (?,∞) is expressed (b, infty), and an answer of the form (−∞,?)∪(?,∞) is expressed (-infty, a)U(b, infty).

B. The rejection region for the standardized test statistic:

C. The p-value is

2)The contents of 32 cans of Coke have a mean of ?⎯⎯⎯=12.15 and a standard deviation of ?=0.13 Find the value of the test statistic ? for the claim that the population mean is ?=12.

3)Given the significance level ?=0.07 find the following:

(a)    left-tailed ? value
?=

(b)    right-tailed ? value
?=

(c)    two-tailed ? value
|?|=

Answer 1

Question 1

Test Statistic :-
t = ( X̅ - µ ) / ( S / √(n))
t = ( 20.2 - 20 ) / ( 2.9364 / √(10) )
t = 0.2154

Test Criteria :-
Reject null hypothesis if | t | > t(α/2, n-1)
Critical value t(α/2, n-1) = t(0.08 /2, 10-1) = ±1.973

(-infty, a-1.973) U (1.973, infty)

P - value = P ( t > 0.2154 ) = 0.8343

Question 2

Test Statistic :-
t = ( X̅ - µ ) / ( S / √(n))
t = ( 12.15 - 12 ) / ( 0.13 / √(32) )
t = 6.5271

Question 3

Part a)

Critical value Z(α) = Z(0.07) = -1.476

Part b)

Critical value Z(α) = Z(0.07) = 1.476

Part c)

Critical value Z(α/2) = Z( 0.07 /2 ) = 1.812