A random sample of 50 students was asked to estimate how much money they spent on textbooks in a year. The sample skewness of these amounts was found to be 0.83 and the sample kurtosis was 3.98. Test at the 10% level the null hypothesis that the population distribution of amounts spent is normal.

A random sample of 150 residents in one community was asked to indicate their first preference for one of three television stations that air the 5 p.m. news. The results obtained are shown in the following table. Test the null hypothesis that for this population their first preferences are evenly distributed over the three stations.

$$\begin{array}{lccc} \hline \text { Station } & \text { A } & \text { B } & \text { C } \\ \hline \text { Number of first preferences } & 47 & 42 & 61 \\ \hline \end{array}$$

The Gallup Poll once asked a random sample of 1540 adults, " Do you happen to jog?" Suppose that in fact 15% of all adults jog. Find the mean and standard deviation of the proportion

$$\hat{p}$$

of the sample who jog.(Assume the sample is an SRS)

Consider the conjecture.
If $\triangle \mathrm{MNO}$ is an acute triangle, $\mathrm{D}$ lies on $\overline{\mathrm{MN}}$, and $\mathrm{E}$ lies on $\overline{\mathrm{MO}}$, then $\triangle \mathrm{MDE}$ is an acute triangle.
What is the hypothesis of the conjecture? What is its conclusion?

The Gallup Poll once asked a random sample of 1540 adults, "Do you happen to jog?" Suppose that in fact 15% of all adults jog. Find the mean and standard deviation of the proportion $\hat{p}$ of the sample who jog. (Assume the sample is an SRS.)

Suppose that you want to perform a hypothesis test based on independent simple random samples to compare the means of two populations. Assume that the variable under consideration is normally distributed on each of the two populations and that the population standard deviations are unequal. a. Identify the procedures discussed in this chapter that could be used to carry out the hypothesis test, that is, the procedures whose assumptions are satisfied. b. Among the procedures that you identified in part (a), which is the best one to use? Explain your answer.

If 100 flips of a coin result in 30 heads and 70 tails, can we assert on the 5% level that the coin is fair? What would be the smallest number of heads in above under which the hypothesis "Fair coin" is still accepted (with $\alpha=5 \%$ )?

The "snout" of a frog tadpole bears a sucker. A salamander tadpole has a mustache-shaped structure called a balancer in the same area. Suppose that you perform an experiment in which you transplant ectoderm from the side of a young salamander embryo to the snout of a frog embryo. The tadpole that develops has a balancer. When you transplant ectoderm from the side of a slightly older salamander embryo to the snout of a frog embryo, the frog tadpole ends up with a patch of salamander skin on its snout. Suggest a hypothesis to explain these results in terms of developmental mechanisms. How might you test your hypothesis?

The Brennans are planning to buy a house $4$ years from now. Housing experts in their area have estimated that the cost of a home will increase at a rate of $3\%$ per year during that $4$-year period. If their predictions are correct, how much can the Brennans expect to pay for a house that currently costs $\$300,000$?

The following exercises describe the results of a hypothesis test in terms of the probability of obtaining a particular sample. In each case, use the given context to formulate the null and alternative hypotheses. Then discuss whether the sample provides evidence for rejecting or not rejecting the null hypothesis.

Each baseball in a random sample of $40$ new balls is dropped onto a concrete surface and the bounce height is recorded. The heights have a mean of $92.67$ inches (based on data from USA Today). A statistically literate manager claims that the mean bounce height for all baseballs is $90.10$ inches and the probability of observing a sample mean of $92.67$ is $0.035$.

Lovato Motors Inc. has cash flows from operating activities of $720,000. Cash flows used for investments in property, plant, and equipment totaled$440,000, of which 85% of this investment was used to replace existing capacity.

Determine the free cash flow for Lovato Motors Inc.

Curwen Inc. reported net cash flow from operating activities of $357,500 on its statement of cash flows for the year ended December 31, 2014. The following information was reported in the Cash Flows from Operating Activities section of the statement of cash flows, using the indirect method:

$$\begin{array}{llr} \text{Decrease in income taxes payable}&\text{\$7,700}\\ \text{Decrease in inventories}&\text{19,140}\\ \text{Depreciation}&\text{29,480}\\ \text{Gain on sale of investments}&\text{13,200}\\ \text{Increase in accounts payable}&\text{5,280}\\ \text{Increase in prepaid expenses}&\text{2,970}\\ \text{Increase in accounts receivable}&\text{14,300}\\ \end{array}$$

a. Determine the net income reported by Curwen Inc. for the year ended December 31, 2014.

The area labeled “Economic profit” can be found by multiplying the difference between P and ATC by quantity. It also can be found by:

a. dividing profit per unit by quantity.

b. subtracting total cost from total revenue.

c. multiplying the coefficient of demand elasticity by quantity.

d. multiplying the difference between P and MC by quantity.