**Null and Alternative Hypotheses**

## You are testing that the mean speed of your cable Internet connection is more than three Megabits per

## second. State the null and alternative hypotheses. What is the Ho and H1

## Q2

## A sociologist claims the probability that a person picked at random in Times Square in New York City is

## visiting the area is 0.83. You want to test to see if the claim is correct. State the null and alternative

## hypotheses. What is the Ho and H1

## Q3

## A hospital is trying to cut down on emergency room wait times. It is interested in the amount of time

## patients must wait before being called back to be examined. An investigation committee randomly

## surveyed 70 patients. The sample mean was 1.5 hours with a sample standard deviation of 0.5 hours.

## Identify the following:

## a. x = ____

## b. sx = ____

## c. n = ____

## d. n – 1 = ____

## Q4

## A hospital is trying to cut down on emergency room wait times. It is interested in the amount of time

## patients must wait before being called back to be examined. An investigation committee randomly

## surveyed 70 patients. The sample mean was 1.5 hours with a sample standard deviation of 0.5 hours.

## Construct a 95% confidence interval for the population mean time spent waiting.

## Ans: CI: (1.3808 and 1.6192) Show your workings

## Q5

## One hundred eight Americans were surveyed to determine the number of hours they spend watching

## television each month. It was revealed that they watched an average of 151 hours each month with a

## standard deviation of 32 hours. Assume that the underlying population distribution is normal.

## Find the 99% confidence interval for the population mean hours spent watching television per month.

## Ans; CI: (142.92 and 159.08) Show your workings

## Q6

## The systolic blood pressure (given in millimeters) of males has an approximately normal distribution with

## mean μ = 125 and standard deviation σ = 14. Systolic blood pressure for males follows a normal

## distribution. Calculate the z-scores for the male systolic blood pressures 100 and 150 millimeters.

## Ans: Z = -1.8 and 1.8

## Q7

## A baker is deciding how many batches of muffins to make to sell in his bakery. He wants to make enough to

## sell everyone and no less. Through observation, the baker has established a probability distribution.

## x P(x)

## 1 0.15

## 2 0.35

## 3 0.40

## 4 0.10

## What is the probability the baker will sell more than one batch? P (x > 1)

## Ans: 0.85 (Show your workings)

## Q8

## A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their

## product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices.

## Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the

## data below:

## City Price ($) Sales

## River City 1.30 100

## Hudson 1.60 90

## Ellsworth 1.80 90

## Prescott 2.00 40

## Rock Elm 2.40 38

## Stillwater 2.90 32

## what is the coefficient of correlation for these data? Ans= -0.8854 (Show detailed workings)

## Q9

## Suppose that history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be

## selected.

## (a) Find the mean of this binomial distribution (Ans=3) (Show your solution)

## (b) Find the variance of the binomial distribution (Ans=1.2) (Show your solution)

## Q10

## A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line

## table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of

## this table saw is taken. The probability that the sample mean will be greater than 88 minutes is ________.

## Answer: 0.0548 (Show your solution)

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