The average amount of time it takes for couples to further communicate with each other after their first date has ended is 3.06 days. Is this average shorter for blind dates? A researcher interviewed 43 couples who had recently been on blind dates and found that they averaged 2.8 days to communicate with each other after the date was over. Their standard deviation was 1.146 days. What can be concluded at the the αα = 0.05 level of significance? For this study, we should use The null and alternative hypotheses would be: H0:H0: H1:H1: The test statistic = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is αα Based on this, we should the null hypothesis. Thus, the final conclusion is that ... The data suggest the populaton mean is significantly less than 3.06 at αα = 0.05, so there is statistically significant evidence to conclude that the population mean time for couples who have been on a blind date to communicate with each other after the date is over is less than 3.06. The data suggest that the population mean is not significantly less than 3.06 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean time for couples who have been on a blind date to communicate with each other after the date is over is less than 3.06. The data suggest the population mean is not significantly less than 3.06 at αα = 0.05, so there is statistically significant evidence to conclude that the population mean time for couples who have been on a blind date to communicate with each other after the date is over is equal to 3.06.

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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The average amount of time it takes for couples to further communicate with each other after their first date has ended is 3.06 days. Is this average shorter for blind dates? A researcher interviewed 43 couples who had recently been on blind dates and found that they averaged 2.8 days to communicate with each other after the date was over. Their standard deviation was 1.146 days. What can be concluded at the the αα = 0.05 level of significance?

For this study, we should use
The null and alternative hypotheses would be:

H0:H0:

H1:H1:

The test statistic = (please show your answer to 3 decimal places.)
The p-value = (Please show your answer to 4 decimal places.)
The p-value is αα
Based on this, we should the null hypothesis.
Thus, the final conclusion is that ...
- The data suggest the populaton mean is significantly less than 3.06 at αα = 0.05, so there is statistically significant evidence to conclude that the population mean time for couples who have been on a blind date to communicate with each other after the date is over is less than 3.06.
- The data suggest that the population mean is not significantly less than 3.06 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean time for couples who have been on a blind date to communicate with each other after the date is over is less than 3.06.
- The data suggest the population mean is not significantly less than 3.06 at αα = 0.05, so there is statistically significant evidence to conclude that the population mean time for couples who have been on a blind date to communicate with each other after the date is over is equal to 3.06.

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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