On average, a banana will last 6 days from the time it is purchased in the store to the time it is too rotten to eat. Is the mean time to spoil less if the banana is hung from the ceiling? The data show results of an experiment with 15 bananas that are hung from the ceiling. Assume that that distribution of the population is normal. 6.3, 3.5, 5.6, 4.2, 4.4, 3.9, 4.5, 5.5, 7.1, 5.6, 6.6, 6.1, 6.3, 7.2, 4 What can be concluded at the the αα = 0.01 level of significance 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 that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is not significantly less than 6 at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is less than 6. The data suggest the population mean is not significantly less than 6 at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is equal to 6. The data suggest the populaton mean is significantly less than 6 at αα = 0.01, so there is statistically significant evidence to conclude that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is less than 6.

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, a banana will last 6 days from the time it is purchased in the store to the time it is too rotten to eat. Is the mean time to spoil less if the banana is hung from the ceiling? The data show results of an experiment with 15 bananas that are hung from the ceiling. Assume that that distribution of the population is normal.

6.3, 3.5, 5.6, 4.2, 4.4, 3.9, 4.5, 5.5, 7.1, 5.6, 6.6, 6.1, 6.3, 7.2, 4

What can be concluded at the the αα = 0.01 level of significance 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 that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is not significantly less than 6 at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is less than 6.
- The data suggest the population mean is not significantly less than 6 at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is equal to 6.
- The data suggest the populaton mean is significantly less than 6 at αα = 0.01, so there is statistically significant evidence to conclude that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is less than 6.

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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