Question

1) The sample mean and standard deviation from a random sample of 22 observations from a normal population were computed as x¯=40 and s = 13. Calculate the t statistic of the test required to determine whether there is enough evidence to infer at the 7% significance level that the population mean is greater than 37.

Test Statistic=

2) The contents of 33 cans of Coke have a mean of x¯=12.15 and a standard deviation of s=0.13. Find the value of the test statistic t for the claim that the population mean is ?=12.

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

14 12 11 18 20 20 19 13 14 17

Test to determine if we can infer at the 3% significance level that the population mean is not equal to 16, 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 (??,a) is expressed (-infty, a), an answer of the form (b,?) is expressed (b, infty), and an answer of the form (??,a)?(b,?) is expressed (-infty, a)U(b, infty).

B. The rejection region for the standardized test statistic:

C. The p-value is

D. Your decision for the hypothesis test:

A. Do Not Reject H0.

B. Reject H1.

C. Do Not Reject H1.

D. Reject H0.

Answer 1

1)

Test statistic = ( x^- - 37 ) / ( s / 22^0.5 ) = ( 40 - 37 ) / ( 13 / 22^0.5 ) = 1.0824

2)

Test statistic = ( x^- - 12 ) / ( s / 33^0.5 ) = ( 12.15 - 12) / ( 0.13 / 33^0.5 ) = 6.628

A. The value of the standardized test statistic = ( x^- - 16 ) / ( s / 10^0.5 )

x^- = mean of x = 15.8

s = standard deviation = 3.3928

The value of the standardized test statistic = ( 15.8 - 16 ) / ( 3.3928 / 10^0.5) = - 0.1864

B.

t_0.05,9 = 2.262

The rejection region for the standardized test statistic : (-infty, -2.262) U (2.262, infty)

C. The p-value = 0.856

D. Your decision for the hypothesis test : A. Do Not Reject H0.