# Statistics Solutions

The questions for the assignment were as follows:

1. In the US legal system, a defendant is presumed innocent until proven guilty. Consider a null hypothesis, Ho: that the defendant is innocent, and an alternative hypothesis, Ha: that the defendant is guilty. Explain the meaning of a jury committing a Type I error and of committing a Type II error.

2. The quality-control manager at a light bulb factory needs to determine whether the mean life of a large shipment of light bulbs is equal to 375 hours. The population standard deviation is 100 hours. A random sample of 64 light bulbs indicates a sample mean life of 350 hours. At a 5% level of significance, is there evidence that the mean life is different from 375 hours? What is your conclusion?

3. The mean waiting time for the drive-through window of a fast-food franchise is believed to be 3.7 minutes. A manager wants to check the time at her particular restaurant. A sample of 75 customers is selected and the sample mean waiting time is 3.57 minutes with a sample standard deviation of 0.8 minutes. Is there evidence that the waiting time at this particular restaurant is less than 3.7 minutes? Use a 1% level of significance. What is your conclusion?

4. The US department of education reports that 46% of full-time college students are employed while attending college. A recent survey of 600 full-time students at CCP found that 305 were employed. At a 5% level of significance, test to see if there is sufficient evidence that the proportion of full-time students who are employed at CCP is greater than 46%. What is your conclusion?

The solution to the first problem is given below. Please purchase the full solutions if you wish to use them.

1. In the US legal system, a defendant is presumed innocent until proven guilty. Consider a null hypothesis, Ho: that the defendant is innocent, and an alternative hypothesis, Ha: that the defendant is guilty. Explain the meaning of a jury committing a Type I error and of committing a Type II error.

A Type I error is when we reject the null hypothesis when it is actually true. This would correspond to the jury finding the defendant guilty even though he or she is innocent. Our legal system is supposed to minimize this type of error in order to minimize unjust incarceration.

A Type II error is when we fail to reject a false null hypothesis. This would correspond to the jury finding a guilty defendant to be innocent. In other words, he or she gets away with the crime.

Other Details about the Project/Assignment
Subjects: Statistics -> Basic Statistics
Topic: Statistics Solutions Chapter 9
Level: College / University
Tags:

### Statistics, solutions, word problems

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Project Details
Subjects: Statistics -> Basic Statistics
Topic: Statistics Solutions Chapter 9
Level: College / University
Tags:

## Statistics, solutions, word problems

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