On average, Americans have lived in 2 places by the time they are 18 years old. Is this average a different number for college students? The 63 randomly selected college students who answered the survey question had lived in an average of 1.97 places by the time they were 18 years old. The standard deviation for the survey group was 0.4. What can be concluded at the αα = 0.10 level of significance? The null and alternative hypotheses would be: H0:H0: ? p μ Select an answer = < > ≠ H1:H1: ? p μ Select an answer ≠ > < = The test statistic ? t or z = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) Interpret the p-value in the context of the study. If the population mean number of places that college students lived in by the time they were 18 years old is 2 and if you survey another 63 college students, then there would be a 55.38136608% chance that the sample mean for these 63 college students would either be less than 1.97 or greater than 2.03. There is a 55.38136608% chance of a Type I error. If the population mean number of places that college students lived in by the time they were 18 years old is 2 and if you survey another 63 college students then there would be a 55.38136608% chance that the population mean would either be less than 1.97 or greater than 2.03. There is a 55.38136608% chance that the population mean number of places that college students lived in by the time they were 18 years old is not equal to 2.

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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On average, Americans have lived in 2 places by the time they are 18 years old. Is this average a different number for college students? The 63 randomly selected college students who answered the survey question had lived in an average of 1.97 places by the time they were 18 years old. The standard deviation for the survey group was 0.4. What can be concluded at the αα = 0.10 level of significance?

The null and alternative hypotheses would be:

H0:H0: ? p μ Select an answer = < > ≠

H1:H1: ? p μ Select an answer ≠ > < =

The test statistic ? t or z = (please show your answer to 3 decimal places.)
The p-value = (Please show your answer to 4 decimal places.)
Interpret the p-value in the context of the study.
- If the population mean number of places that college students lived in by the time they were 18 years old is 2 and if you survey another 63 college students, then there would be a 55.38136608% chance that the sample mean for these 63 college students would either be less than 1.97 or greater than 2.03.
- There is a 55.38136608% chance of a Type I error.
- If the population mean number of places that college students lived in by the time they were 18 years old is 2 and if you survey another 63 college students then there would be a 55.38136608% chance that the population mean would either be less than 1.97 or greater than 2.03.
- There is a 55.38136608% chance that the population mean number of places that college students lived in by the time they were 18 years old is not equal to 2.

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 + ...

Expert Solution

Step 1

Given information-

Population mean, μ = 2

Sample size, n = 63

Sample mean, x-bar = 1.97

Sample standard deviation, s = 0.4

Significance level, α = 0.1

For this steady we will use two tailed t-test statistics.

We have to test the claim that this average is different for college students.

Hypothesis Formulation-

Null Hypothesis, H₀: μ = 2

Alternate Hypothesis, H_a: μ ≠ 2

Since here population standard deviation is unknown so using t-test statistics.

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