Question

z-test statistic for H?: ? = ?? (? known, normal population or large sample): z = (x? - ?) / (? / ?n) (use Table II to find p-values) t-test statistic for H?: ? = ?? (? unknown, normal population or large sample) t = (x? - ?) / (s / ?n) with df = n - 1 (use three page t-distribution table to find p-values) Hypothesis interpretation template: At the [%] significance level, the data [DO / DO NOT] provide sufficient evidence that the mean [variable] [differs from / is larger than / is less than] [mean we are comparing it to]. What if we get z- or t-values outside the values in the tables? • z-values outside of Table II: There is teeny tiny print on the bottom of Table II that says if we find z-scores less than -3.9, then the area to the left of that z-score, rounded to four decimal places, will be 0.0000. • t-values outside of the three-page table: If the t-score is greater than 4.0, the area to the right, rounded to three decimal places, is 0.000. (Or if the t-score is less than -4.0, the area to the right is 1.000 rounded to three decimal places.) 1. The mean age of MSU Denver students is 25. A certain class of 33 students has a mean age of 22.64 years. Assuming a population standard deviation of 2.87 years, at the 5% significance level, do the data provide sufficient evidence to conclude that the mean age of students in this class is less than the MSU Denver mean? a. Set up the hypotheses for the one-mean z-test. H?: H?: b. Compute the test statistic. Round to two decimal places. c. Sketch a normal curve, mark your value from part (b), and shade in the area(s) we are interested in. Determine the p-value. d. Determine if the null hypothesis should be rejected. e. Interpret your result in the context of the problem in a sentence.

          z-test statistic for H?: ? = ??
(? known, normal population or large sample):
z = (x? - ?) / (? / ?n)
(use Table II to find p-values)

t-test statistic for H?: ? = ??
(? unknown, normal population or large sample)
t = (x? - ?) / (s / ?n)
with df = n - 1
(use three page t-distribution table to find p-values)

Hypothesis interpretation template: At the [%] significance level, the data [DO / DO NOT] provide sufficient evidence that the mean [variable] [differs from / is larger than / is less than] [mean we are comparing it to].

What if we get z- or t-values outside the values in the tables?
• z-values outside of Table II: There is teeny tiny print on the bottom of Table II that says if we find z-scores less than -3.9, then the area to the left of that z-score, rounded to four decimal places, will be 0.0000.
• t-values outside of the three-page table: If the t-score is greater than 4.0, the area to the right, rounded to three decimal places, is 0.000. (Or if the t-score is less than -4.0, the area to the right is 1.000 rounded to three decimal places.)

1. The mean age of MSU Denver students is 25. A certain class of 33 students has a mean age of 22.64 years. Assuming a population standard deviation of 2.87 years, at the 5% significance level, do the data provide sufficient evidence to conclude that the mean age of students in this class is less than the MSU Denver mean?
a. Set up the hypotheses for the one-mean z-test.
H?: __________ H?: __________
b. Compute the test statistic. Round to two decimal places.
c. Sketch a normal curve, mark your value from part (b), and shade in the area(s) we are interested in. Determine the p-value.
d. Determine if the null hypothesis should be rejected.
e. Interpret your result in the context of the problem in a sentence.

z-test statistic for H?: ? = ??
(? known, normal population or large sample):
z = (x? - ?) / (? / ?n)
(use Table II to find p-values)

t-test statistic for H?: ? = ??
(? unknown, normal population or large sample)
t = (x? - ?) / (s / ?n)
with df = n - 1
(use three page t-distribution table to find p-values)

Hypothesis interpretation template: At the [%] significance level, the data [DO / DO NOT] provide sufficient evidence that the mean [variable] [differs from / is larger than / is less than] [mean we are comparing it to].

What if we get z- or t-values outside the values in the tables?
• z-values outside of Table II: There is teeny tiny print on the bottom of Table II that says if we find z-scores less than -3.9, then the area to the left of that z-score, rounded to four decimal places, will be 0.0000.
• t-values outside of the three-page table: If the t-score is greater than 4.0, the area to the right, rounded to three decimal places, is 0.000. (Or if the t-score is less than -4.0, the area to the right is 1.000 rounded to three decimal places.)

1. The mean age of MSU Denver students is 25. A certain class of 33 students has a mean age of 22.64 years. Assuming a population standard deviation of 2.87 years, at the 5% significance level, do the data provide sufficient evidence to conclude that the mean age of students in this class is less than the MSU Denver mean?
a. Set up the hypotheses for the one-mean z-test.
H?: H?:
b. Compute the test statistic. Round to two decimal places.
c. Sketch a normal curve, mark your value from part (b), and shade in the area(s) we are interested in. Determine the p-value.
d. Determine if the null hypothesis should be rejected.
e. Interpret your result in the context of the problem in a sentence.

Added by Kelly T.

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