For this study, we should use The null and alternative hypotheses would be: �0: �1: 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 � Based on this, we should the null hypothesis.
For this study, we should use The null and alternative hypotheses would be: �0: �1: 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 � Based on this, we should the null hypothesis.
For this study, we should use The null and alternative hypotheses would be: �0: �1: 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 � Based on this, we should the null hypothesis.
The average number of accidents at controlled intersections per year is 4.5. Is this average more for intersections with cameras installed? The 61 randomly observed intersections with cameras installed had an average of 4.7 accidents per year and the standard deviation was 0.78. What can be concluded at the � = 0.05 level of significance?
For this study, we should use
The null and alternative hypotheses would be:
�0:
�1:
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 �
Based on this, we should the null hypothesis.
Thus, the final conclusion is that ...
The data suggest that the population mean is not significantly more than 4.5 at � = 0.05, so there is statistically insignificant evidence to conclude that the population mean number of accidents per year at intersections with cameras installed is more than 4.5 accidents.
The data suggest that the sample mean is not significantly more than 4.5 at � = 0.05, so there is statistically insignificant evidence to conclude that the sample mean number of accidents per year at intersections with cameras installed is more than 4.7 accidents.
The data suggest that the populaton mean is significantly more than 4.5 at � = 0.05, so there is statistically significant evidence to conclude that the population mean number of accidents per year at intersections with cameras installed is more than 4.5 accidents.
Interpret the p-value in the context of the study.
If the population mean number of accidents per year at intersections with cameras installed is 4.5 and if another 61 intersections with cameras installed are observed then there would be a 2.48710489% chance that the population mean number of accidents per year at intersections with cameras installed would be greater than 4.5.
If the population mean number of accidents per year at intersections with cameras installed is 4.5 and if another 61 intersections with cameras installed are observed then there would be a 2.48710489% chance that the sample mean for these 61 intersections with cameras installed would be greater than 4.7.
There is a 2.48710489% chance that the population mean number of accidents per year at intersections with cameras installed is greater than 4.5 .
There is a 2.48710489% chance of a Type I error.
Interpret the level of significance in the context of the study.
If the population population mean number of accidents per year at intersections with cameras installed is more than 4.5 and if another 61 intersections with cameras installed are observed then there would be a 5% chance that we would end up falsely concluding that the population mean number of accidents per year at intersections with cameras installed is equal to 4.5.
If the population mean number of accidents per year at intersections with cameras installed is 4.5 and if another 61 intersections with cameras installed are observed then there would be a 5% chance that we would end up falsely concluding that the population mean number of accidents per year at intersections with cameras installed is more than 4.5.
There is a 5% chance that you will get in a car accident, so please wear a seat belt.
There is a 5% chance that the population mean number of accidents per year at intersections with cameras installed is more than 4.5.
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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