The average number of accidents at controlled intersections per year is 5.7. Is this average less for intersections with cameras installed? The 58 randomly observed intersections with cameras installed had an average of 5.4 accidents per year and the standard deviation was 1. What can be concluded at the αα = 0.10 level of significance?

For this study, we should use Select an answer z-test for a population proportion t-test for a population mean

The null and alternative hypotheses would be:

H0:H0:  ? p μ  Select an answer = > ≠ <

H1:H1:  ? μ p  Select an answer ≠ > < =

The test statistic ? z t  =  (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 Select an answer reject accept fail to reject  the null hypothesis.

Thus, the final conclusion is that ...

The data suggest that the population mean is not significantly less than 5.7 at αα = 0.10, so there is statistically insignificant evidence to conclude that the population mean number of accidents per year at intersections with cameras installed is less than 5.7 accidents.

The data suggest that the populaton mean is significantly less than 5.7 at αα = 0.10, so there is statistically significant evidence to conclude that the population mean number of accidents per year at intersections with cameras installed is less than 5.7 accidents.

The data suggest that the sample mean is not significantly less than 5.7 at αα = 0.10, so there is statistically insignificant evidence to conclude that the sample mean number of accidents per year at intersections with cameras installed is less than 5.4 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 5.7 and if another 58 intersections with cameras installed are observed then there would be a 1.30352362% chance that the population mean number of accidents per year at intersections with cameras installed would be less than 5.7.

There is a 1.30352362% chance that the population mean number of accidents per year at intersections with cameras installed is less than 5.7.

There is a 1.30352362% chance of a Type I error.

If the population mean number of accidents per year at intersections with cameras installed is 5.7 and if another 58 intersections with cameras installed are observed then there would be a 1.30352362% chance that the sample mean for these 58 intersections with cameras installed would be less than 5.4.

Interpret the level of significance in the context of the study.

There is a 10% chance that the population mean number of accidents per year at intersections with cameras installed is less than 5.7.

There is a 10% chance that you will get in a car accident, so please wear a seat belt.

If the population mean number of accidents per year at intersections with cameras installed is 5.7 and if another 58 intersections with cameras installed are observed then there would be a 10% chance that we would end up falsely concluding that the population mean number of accidents per year at intersections with cameras installed is less than 5.7.

If the population population mean number of accidents per year at intersections with cameras installed is less than 5.7 and if another 58 intersections with cameras installed are observed then there would be a 10% 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 5.7.

Name: The average number of accidents at controlled intersections per year i
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: The average number of accidents at controlled intersections per year is 5.7. Is this average less for intersections with cameras installed? The 58 randomly observed intersections with cameras installed had an average of 5.4 accidents per year and th

Question

The average number of accidents at controlled intersections per year is 5.7. Is this average less for intersections with cameras installed? The 58 randomly observed intersections with cameras installed had an average of 5.4 accidents per year and the standard deviation was 1. What can be concluded at the αα = 0.10 level of significance?

For this study, we should use Select an answer z-test for a population proportion t-test for a population mean
The null and alternative hypotheses would be:

H0:H0: ? p μ Select an answer = > ≠ <

H1:H1: ? μ p Select an answer ≠ > < =

The test statistic ? z t = (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 Select an answer reject accept fail to reject the null hypothesis.
Thus, the final conclusion is that ...
- The data suggest that the population mean is not significantly less than 5.7 at αα = 0.10, so there is statistically insignificant evidence to conclude that the population mean number of accidents per year at intersections with cameras installed is less than 5.7 accidents.
- The data suggest that the populaton mean is significantly less than 5.7 at αα = 0.10, so there is statistically significant evidence to conclude that the population mean number of accidents per year at intersections with cameras installed is less than 5.7 accidents.
- The data suggest that the sample mean is not significantly less than 5.7 at αα = 0.10, so there is statistically insignificant evidence to conclude that the sample mean number of accidents per year at intersections with cameras installed is less than 5.4 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 5.7 and if another 58 intersections with cameras installed are observed then there would be a 1.30352362% chance that the population mean number of accidents per year at intersections with cameras installed would be less than 5.7.
- There is a 1.30352362% chance that the population mean number of accidents per year at intersections with cameras installed is less than 5.7.
- There is a 1.30352362% chance of a Type I error.
- If the population mean number of accidents per year at intersections with cameras installed is 5.7 and if another 58 intersections with cameras installed are observed then there would be a 1.30352362% chance that the sample mean for these 58 intersections with cameras installed would be less than 5.4.
Interpret the level of significance in the context of the study.
- There is a 10% chance that the population mean number of accidents per year at intersections with cameras installed is less than 5.7.
- There is a 10% chance that you will get in a car accident, so please wear a seat belt.
- If the population mean number of accidents per year at intersections with cameras installed is 5.7 and if another 58 intersections with cameras installed are observed then there would be a 10% chance that we would end up falsely concluding that the population mean number of accidents per year at intersections with cameras installed is less than 5.7.
- If the population population mean number of accidents per year at intersections with cameras installed is less than 5.7 and if another 58 intersections with cameras installed are observed then there would be a 10% 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 5.7.

Accepted Answer

“Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

The test statistic ? z t = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is ? > ≤ αα