Statistics and Probability Answers

As a counselor in the field of addiction, you are interested in researching if online gambling is becoming more prevalent. You decide to conduct research to compare online gambling to gambling in public places such as casinos. You hypothesize that online gambling is more prevalent among those who are under the age 30, leading to more online gambling addictions in those individuals who are under 30. To test your hypothesis, you use a random sample of 40 individuals who report attending counseling because of a gambling addiction. The ages of the individuals and initial mode of gambling was recorded. The ages for those who gamble online and in public are shown in the table. On the basis of the data provided, can you conclude that online gambling is more prevalent among individuals who are under the age of 30 at a level of significance of 0.05? Why or why not? (Show all seven steps of the appropriate hypothesis test.)

The weight of new born babies is normally distributed with a mean of 3.3Kg and a standard deviation of 1.2 Kg. Find the percentage of new born babies between 2 kg and 4 kg

Engineers for a cell phone producer think that using Bluetooth decreases battery life. Average battery life is expected to be 23 hours. A sample of 20 phones was tested for battery life with Bluetooth enabled. The average for the sample was 22.5 hours with a standard deviation of 0.9 hours.

What is the null hypothesis?

What is the alternative hypothesis?

What is the test statistic t ?

What is the t value for a .05 one tailed critical (rejection) region?

Draw the rejection region.


Do you reject or fail to reject the null hypothesis? Show why you made your choice.


What is the approximate p value for the test?

For the confidence interval below, what is the sample mean, ?
18 < u < 24

In a random sample of 12 residents of Brooksville the mean waste recycled per person was 1.3 pound with a standard deviation of 0.25 pounds. What is the 80% confidence interval for the mean waste recycled per person?

From a sample of 10 squirrels the average weight was 511 grams with standard deviation of 160 grams.

What is the t value for a 95% confidence interval?


What are the lower and upper limits of the 95% confidence interval?

A statistical process analyst is responsible for assuring statistical control. In one process, a machine is supposed to drop 11.4 ounces of mints into a bag. (Assume that this process can be approximated by a normal distribution). The acceptable ranges for weights of the bags of mints are 11.25 ounces to 11.55 ounces, inclusive.

An error with the release valve has caused the setting on the mint release machine to “shift”. Assume that the machine shift is filling the bags with a mean weight of 11.56 ounces and a standard deviation of 0.05 ounces. To check that the machine is placing the correct weight of mints into the bags, you randomly select three samples of five bags each and find the mean weight in ounces for each sample.

Respond to the following:
1.While sampling individual bags:
◦You randomly select a bag of mints. What is the probability that the bag you select is not outside the acceptable range? (That is, you do not detect that the machine has shifted.)
◦You randomly select 15 bags of mints. What is the probability that you select at least one bag that is not outside the acceptable range?


2.While sampling groups of five:
◦You randomly select a sample of five bags. What is the probability that your sample of five bags has a mean that is not outside the acceptable range? (That is, you do not detect that the machine has shifted.)
◦You randomly select three samples of five bags. What is the probability that you select at least one sample of five bags that has a mean that is not outside the acceptable range?



3.Describe your solutions to each of these problems and explain whether taking 15 bags of mints in one sample or three samples of five bags each is the better way to test for a process that is out of statistical control.

A study of 35 golfers showed that their average score on a particular course was 92. The sample standard deviation was 5. What is the best point estimate of the mean?

For the confidence interval below, what is the sample mean, ?

18 < u < 24

Engineers for a cell phone producer think that using Bluetooth decreases battery life. Average battery life is expected to be 23 hours. A sample of 20 phones was tested for battery life with Bluetooth enabled. The average for the sample was 22.5 hours with a standard deviation of 0.9 hours.

What is the null hypothesis?

What is the alternative hypothesis?

What is the test statistic t ?

What is the t value for a .05 one tailed critical (rejection) region?


Draw the rejection region.