Math Answers

Test the hypothesis. Show the step-by-step process in testing hypothesis.

1. A researcher claims that the average salary of a private school teacher is greater than P35,000 with a standard deviation of P7,000. A sample of 35 teachers has a mean salary of P37,000. Test the claim of the researcher. At 0.05 level of significance, test the claim of the researcher.

2. A researcher reports that the average salary of a college dean is more than P65,000. A sample of 35 college deans has a mean salary of P67,000. At 0.01 level of significance, test the claim that the college deans earn more than P65,000 a month. The standard deviation of the population is P5,250.

1. A study shows that the average daily coffee consumption of a 20-30 years old students is 3 cups per day. A university claims that their students tend to drink less than 3 cups. They selected 20 students and found the mean of 3.5 with a standard deviation of 1.5 cups. Use 0.01 level of significance to test their claim.

Answer the following:

Parameter:

Claim:

Claim ( in symbol ):

Ho: Ho:

Ha: Ha:

What is the significance level or a?

Is it two-tailed or one-tailed test?

A pair of die is rolled, what is the probability of getting a 5 or a 6?

There are five cards in a box containing the numbers 1, 3, 5, 7, and 9. A sample of size 3 is

to be drawn at a time. List all possible sample size of 3 from this population and compute the

mean and variance of the sampling distribution of the sample means.

1. Compute the population mean.

1. Compute the population variance.

1. Determine the number of possible samples.

1. List all possible samples and their corresponding means.

1. Construct the sampling distribution of the sample means.

1. Compute the mean of the sampling distribution of the sample means.

1. Compute the variance of the sampling distribution of the sample means.

1. Construct the histogram.

2. A line for tickets to a local concert had an average waiting time of 20 min. and a σ = 4 min. a. What percentage of the people in line will wait for more than 28 minutes? b. If 2000 ticket buyers were in line, how many of them would expect to wait for less than 16 minutes? c. How many minutes of waiting time would include 95% of those who would fall in line?

TR = 20Q - 4Q

TC = 16 - Q

How many units should be produced to maximise the profit?

Q = 12000 - 60P

C (Q) = 10000 + 4Q

What is the company's profit function?

A basket has 12 marigolds and 8 carnations. if we had picked two flowers one by one with replacement, find the probability of getting a marigold and a carnation.

An automobile traveling at the rate of 20 m/s is approaching an intersection. When the automobile is 100 meters from the intersection, a truck traveling at the rate of 40 m/s crosses the intersection. The automobile and the truck are on perpendicular roads. How fast is the distance between the truck and the automobile changing two seconds after the truck leaves the intersection?

On average, four students visits the Mathematics and Statistics tutoring centre during a 5-minute period.

(a) Calculate the probability that three students visit the centre during a 5 minute period. (3)

(b) During a ten-minute period, what is the probability that at least 4 students visit the centre? (5)