A student at a four-year college claims that mean enrollment at four-year colleges is higher than at two-year colleges in the United States. Two surveys are conducted. Of the 35 four-year colleges surveyed, the mean enrollment was 5,882 with a standard deviation of 745. Of the 35 two-year colleges surveyed, the mean enrollment was 5,200 with a standard deviation of 700. Test the student's claim at the 0.1 significance level. Preliminary: Is it safe to assume that n4yr≤5%n4yr≤5% of all students enrolled at a 4-year college in the Unites States and n2yr≤5%n2yr≤5% of all enrolled at a 2-year college in the Unites States? Yes No Is n4yr≥30n4yr≥30 and n2yr≥30n2yr≥30 ? Yes No Test the claim: Determine the null and alternative hypotheses. H0H0: μ4yrμ4yr μ2yrμ2yr HaHa: μ4yrμ4yr μ2yrμ2yr Determine the test statistic. Round to four decimal places. t=t= Find the pp-value. Round to 4 decimals. pp-value = Make a decision. Reject the null hypothesis. Fail to reject the null hypothesis. Write the conclusion. There is not sufficient evidence to support the claim that enrollement is higher at a four-year college than a two-year college. There is sufficient evidence to support the claim that enrollement is higher at a four-year college than a two-year college.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section: Chapter Questions

Problem 8SGR

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A student at a four-year college claims that mean enrollment at four-year colleges is higher than at two-year colleges in the United States. Two surveys are conducted. Of the 35 four-year colleges surveyed, the mean enrollment was 5,882 with a standard deviation of 745. Of the 35 two-year colleges surveyed, the mean enrollment was 5,200 with a standard deviation of 700. Test the student's claim at the 0.1 significance level.

Preliminary:

Is it safe to assume that

n4yr≤5%n4yr≤5% of all students enrolled at a 4-year college in the Unites States and
n2yr≤5%n2yr≤5% of all enrolled at a 2-year college in the Unites States?
- Yes
- No
Is n4yr≥30n4yr≥30 and n2yr≥30n2yr≥30 ?
- Yes
- No

Test the claim:

Determine the null and alternative hypotheses.

H0H0: μ4yrμ4yr μ2yrμ2yr
HaHa: μ4yrμ4yr μ2yrμ2yr
Determine the test statistic. Round to four decimal places.
t=t=
Find the pp-value. Round to 4 decimals.
pp-value =
Make a decision.
- Reject the null hypothesis.
- Fail to reject the null hypothesis.
Write the conclusion.
- There is not sufficient evidence to support the claim that enrollement is higher at a four-year college than a two-year college.
- There is sufficient evidence to support the claim that enrollement is higher at a four-year college than a two-year college.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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