Statistics and Probability Answers

An electrical firm manufactures light bulb that has a length of life that is approximately normally distributed with a mean of 800 hours and a standard deviation of 40 hours. The supervising electrical Engineer took a random sample of 30 bulbs with an average life of 788 hours, test the hypothesis that µ=800 hours against the alternative hypothesis µ is greater than 800.

Use confidence level of 96%.

Is it a two tailed or one tailed test?

Null hypothesis?

Alternative hypothesis?

Size of the test?

Test statistics?

Critical region?

Decision ( accept or reject null hypothesis)?

The population of each room in a classroom consist of the numbers 10, 11, 15, and 9. List all the sample size of 3 from this population and compute the mean of each sample

The prevalence of a certain type of cancer among men aged 55−𝟔𝟎 is 1 in 100. A blood test will

be positive 95% of the time if the cancer is present but it is also positive 4% of the time if the

cancer is not present.

2.1. In a routine checkup, 56-year-old men receive a positive blood test. What is the probability that

he has the type of cancer?

2.2. What is the probability that a randomly selected 56-year-old men tests negative?

An oil company sends out monthly statements to its customers who purchased gasoline and other items using the company’s credit card. Until now, the company has not included a pre-addressed envelope for returning payments. The mean number of days before payment is received is 9.8. As an experiment to determine whether enclosing pre-addressed envelopes speeds up payment, 150 customers selected at random were sent pre-addressed envelopes with their bills. The sample statistics showed a mean of 9.16 days and a standard deviation of 2.642 days. Do the data provide sufficient evidence at 5% level of significance to establish that enclosure of pre-addressed envelopes improves the average speed of payments?

A manufacturer of light bulbs claims that its light bulbs have a mean life of 2000 hours with a standard deviation of 2. A random sample of 200 such bulbs is selected for testing. If the sample produces a mean value of 1992 hours and a sample standard deviation of 81, is there sufficient evidence to claim that the mean life is significantly less than the manufacturer claimed at 5% significant level

A school has 1000 students. The principal of the school thinks that the average IQ of its students is at least 110. To prove her point, she administers an IQ test to 200 randomly selected students. Among the sampled students, the average IQ is 108 with a standard deviation of 10. Based on these results, should the principal accept or reject her original hypothesis? Assume a significance level of 1%

In a certain Algebra 2 class of 29 students, 18 of them play basketball and 5 of them play baseball. There are 9 students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?

f(x) = kx * e ^ (- x / 2); k is a constant, x > 0 a) Find the value of k for f(x) to be a valid probability function