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Name: A researcher is interested in finding a 95% confidence interval for th
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Description: A researcher is interested in finding a 95% confidence interval for the mean number of times per day that college students text. The study included 104 students who averaged 45.1 texts per day. The standard deviation was 12.8 texts. Round answers to

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A researcher is interested in finding a 95% confidence interval for the mean number of times per day that college students text. The study included 104 students who averaged 45.1 texts per day. The standard deviation was 12.8 texts. Round answers to 3 decimal places where possible.

a. To compute the confidence interval , (which one should be used t or z) distribution.

b. With 95% confidence the population mean number of texts per day is between and texts.

c. If many groups of 104 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population number of texts per day and about percent will not contain the true population mean number of texts per day.

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:

Confidence level = 95% = 0.95

Sample size (n) = 104

Sample mean ( $\bar{x}$ ) = 45.1

Sample Standard deviation (s) = 12.8

Significance level $α = 1 - 0.95 = 0.05$

(a) To compute the confidence interval, we use t-distribution. Since, population standard deviation is not known.

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