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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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Part 1

a. If you test the null hypothesis at the

0.10

level of significance, is there evidence that the population mean wait time is less than

minutes?

State the null and alternative hypotheses.

H0:

μ<25

H1:

μ>25

H0:

μ≥25

H1:

μ<25

H0:

μ<25

H1:

μ≥25

H0:

μ>25

H1:

μ<25

H0:

μ≠25

H1:

μ≥25

H0:

μ≥25

H1:

μ≠25

Part 2

Find the test statistic for this hypothesis test.

tSTAT=enter your response here

(Type an integer or a decimal. Round to two decimal places as needed.)

Part 3

Find the p-value.

The p-value is

enter your response here.

(Type an integer or a decimal. Round to three decimal places as needed.)

Part 4

Is there sufficient evidence to reject the null hypothesis? (Use a

0.10

level of significance.)

Reject

the null hypothesis. There is

sufficient

evidence at the

0.10

level of significance that the population mean wait time is greater than

minutes.

Do not reject

the null hypothesis. There is

insufficient

evidence at the

0.10

level of significance that the population mean wait time is greater

Reject

the null hypothesis. There is

sufficient

evidence at the

0.10

level of significance that the population mean wait time is less than

minutes.

Do not reject

the null hypothesis. There is

insufficient

evidence at the

0.10

level of significance that the population mean wait time is less than

minutes.

Part 5

b. Interpret the meaning of the p-value in this problem.

Choose the correct answer below.

The p-value is the probability that the actual mean wait time is

23.04

minutes or less.

The p-value is the probability that the actual mean wait time is

minutes given the sample mean wait time is

23.04

minutes.

The p-value is the probability that the actual mean wait time is more than

23.04

minutes.

The p-value is the probability of getting a sample mean wait time of

23.04

minutes or less if the actual mean wait time is

minutes.

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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