Statistics and Probability Answers

1.     The owner of a theme park would like to know the average amount of time visitors spend there. To do this, he asked 25 of them and found out that they stayed for an average of 123.5 minutes with a standard deviation of 10.5 minutes. With a confidence level of 95 percent, determine the confidence interval estimate of the population mean.

Suppose we wish to test Ho: µ = 47 versus Ha: µ > 47. What will result if we conclude that the mean is greater than 47 when its true value is really 52?

Q: Suppose a dataset has 8500 email collection. Among 8500 emails, 4000 emails are not-spam and remaining are spam emails. The word “dating” is used as a feature, whose frequency/count in spam emails are 310 and 106 in not-spam emails. You have to compute two probabilities using bayes theorem, only knowing it contains the word “dating”.

First: Probability of an email being spam?        Second: Probability of an email being not spam?

Q: A certain virus infects one in every 20 people. A test used to detect the virus in a person delivers positive outcome at 85% accuracy for infected persons. Moreover, it provides negative outcome for healthy persons at 95% accuracy. Compute followings:

a)     Find the probability that a person has the virus given that his test outcome is positive.

b)     Find the probability that a person does not have the virus given that his test outcome is negative.

c)     Find the probability that a person has the virus given that his test outcome is negative.

3. A diet clinic states that there is an average loss of 24 pounds for those who stay on the program for 20 weeks. The standard deviation is 5 pounds. The clinic tries a new diet, reducing salt intake to see whether that strategy will produce a greater weight loss. A group of 40 volunteers loses as as average of 16.3 pounds each over 20 weeks. Should the clinic change the new diet? Use a 0.05

The owner of a factory that sells a particular bottled fruit juice claims that the average capacity of their products is 250 ml.to test the claim, a consumer group gets a sample of 100 such bottles, calculate the capacity of each bottle, and then the finds mean capacity to be 248 ml. The standard deviation is 5 ml. Is the claim true? Conduct a hypothesis testing using a=0.05.

1. Describe the population parameter of intersect.

2. Formulate the null and alternative hypothesis.

3.what is the appropriate form of test statistic to be used.

4. Identify the appropriate rejection region.

5.compute for the test statistic.(show solution)

6.Make a decision based on the computed value of z and the critical region.

A manufacturer of ball pens claims that a certain pen they manufactures has a mean writing life of 400 pages. A purchasing agent selects a sample of 100 pens and puts them for test. The mean writing life from the sample was 390 pages with a standard deviation of 30 at alpha 0.01.

A school teacher suspects the claim that the mean number of students that use library materials in a certain school is at most 450. To check the claim, the professor checks a random sample of 100 library records and obtain that the mean number of students using library materials is 458 with a standard deviation of 9. What would be the teacher's conclusion using 0.05 level of significance?

a. State the null and alternative hypothesis in symbols.

b. Choose the test statistic applied where 𝛼 = 0.05

c. Determine the critical points

d. Computation of the test statistic

e. Decision

f. Conclusion

Bhartdarshan’ is an Internet-based travel agency wherein customers can see videos of the

cities they plan to visit. The number of hits daily is a normally distributed random variable

with a mean of 10,000 and a standard deviation of 2,400.

a. What is the probability of getting more than 12,000 hits?

b. What is the probability of getting fewer than 9,000 hits?

Scores on a scholarship aptitude exam are normally distributed with a mean of 72 and a standard deviation of 8. What is the lowest score that will place an applicant at the top 10% of the distribution?