Chemical analyses of 1599 red and 4898 white Italian wines showed the next summary statistics for $\mathrm{pH}$ (a measure of acidity):

Type	Count	Mean	St Dev
Red	1599	3.311	0.154
White	4898	3.188	0.151

Is there a difference in $\mathrm{pH}$ between red and white wines?

d) Is there a significant difference in $\mathrm{pH}$ ?

In an introductory statistics course, x = midterm exam score and y = fina l exam score. Both have 1n ean = 80 and standard deviation = 10. The correlation between the exam scores is 0.70.

a. Find the regression equation .

b. Find the predicted final exam score for a student with midterm exam score = 80 and another with midterm exam score = 90.

Determine whether a normal sampling distribution can be used. If can be used, test the claim about the difference between two population proportions

$$p _ { 1 }$$

and

$$p _ { 2 }$$

at the level of significance

$$\alpha$$

. Assume the samples are random and independent. Claim:

$$p _ { 1 } = p _ { 2 }; \alpha = 0.10$$

. Sample statistics:

$$x _ { 1 } = 42, n _ { 1 } = 150$$

and

$$x _ { 2 } = 76, n _ { 2 } = 200$$

In writing about experiments on the scattering of $\alpha$ particles in helium Rutherford said, "On account of the impossibility of distinguishing between the scattered alpha particles and the projected He nuclei, the results are subject to a certain ambiguity." Explain how an awareness of quantum statistics could have removed the ambiguity. What determines whether a gas obeys Bose or Fermi distributions?

(a) Use Excel's Data Analysis > Random Numbers to generate 100 Poisson-distributed random numbers with a mean of $\lambda=4$.

(b) Make a histogram of your sample and assess its shape.

(c) Calculate descriptive statistics. Are the sample mean and standard deviation close to their intended values $\lambda=4$ and $\sigma=\sqrt{\lambda}=\sqrt{4}=2$ ?

(d) Use a $z$ test

$$z=\frac{\bar{x}-\mu}{\sigma / \sqrt{n}}=\frac{\bar{x}-4}{2 / \sqrt{100}}=5 \bar{x}-20$$

to compare the sample mean to the desired mean. Note: Use $z$ instead of $t$ because the hypothesized mean $\mu=4$ and standard deviation $\sigma=2$ are known.

(e) What would happen if 100 statistics students performed similar experiments, assuming that Excel's random number generator is working correctly?

Chemical analyses of 1599 red and 4898 white Italian wines showed the next summary statistics for $\mathrm{pH}$ (a measure of acidity):

Is there a difference in $\mathrm{pH}$ between red and white wines?

a) Write the null and alternative hypotheses

The test scores for a large statistics class have an unknown distribution with a mean of 70 and a standard deviation of 10 . a. Determine the value of $k$ such that at least $50$k$standard deviations from the mean. b. Calculate$k$so that no more than$10 percent of the scores are more than $k percent above the mean.

Use the following data set. The data represent the heights (in inches) of students in a statistics class.

$$\begin{array}{llllllllll}52 & 54 & 55 & 56 & 56 & 56 & 58 & 59 & 60 & 61 \\ 61 & 63 & 65 & 67 & 68 & 68 & 70 & 71 & 72 & \end{array}$$

Find the height that corresponds to the third quartile.

Determine whether a normal sampling distribution can be used. If can be used, test the claim about the difference between two population proportions

$$p _ { 1 }$$

and

$$p _ { 2 }$$

at the level of significance

$$\alpha$$

. Assume the samples are random and independent. Claim:

$$p _ { 1 } < p _ { 2 }; \alpha = 0.05$$

. Sample statistics:

$$x _ { 1 } = 471, n _ { 1 } = 785$$

and

$$x _ { 2 } = 372, n _ { 2 } = 465$$

Population Statistics The table shows the life expectancy of a child (at birth) in the United States for selected years from 1920 to 2000. (Source: U.S. National Center for Health Statistics, U.S. Census Bureau)

$$\begin{array}{|c|c|} \hline \text { Year, } t & \text { Life expectancy, } y \\ \hline 1920 & 54.1 \\ 1930 & 59.7 \\ 1940 & 62.9 \\ 1950 & 68.2 \\ 1960 & 69.7 \\ 1970 & 70.8 \\ 1980 & 73.7 \\ 1990 & 75.4 \\ 2000 & 77.1 \\ \hline \end{array}$$

A model for the life expectancy during this period is

$$y=-0.0025 t^2+0.572 t+44.31$$

where $y$ represents the life expectancy and $t$ is the time in years, with $t=20$ corresponding to 1920 .

Use the graph of the model to estimate the life expectancy of a child for the years 2005 and 2010.

Phytopigments are a marker of the amount of organic matter that settles in sediments. Phytopigment concentrations in deep-sea sediments collected world-wide showed a very strong right-skew. Of these two summary statistics, 0.015 and 0.009 grams per square meter of bottom surface, which one is the mean and which one is the median? Explain your reasoning.

Perform each of the following steps.

a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Find the test value. d. Make the decision. e. Summarize the results.

Use the traditional method of hypothesis testing unless otherwise specified.

According to the Bureau of Transportation Statistics, on-time performance by airlines is described as follows:

Records of 200 randomly selected flights for a major airline company showed that 125 planes were on time; 40 were delayed because of weather, 10 because of a National Aviation System delay, and the rest because of arriving late. At $\alpha=0.05$, do these results differ from the government's statistics?

How do sleep problems affect teenagers? Choose one sleep disorder covered (such as insomnia, nightmares, sleepwalking, apnea, or narcolepsy) and use the Internet to research how the disorder affects teenagers. Look for information on how common the disorder is among teens, recent statistics and data, and common treatments. Write a short report summarizing your findings.

According to a study by Nielsen Mobile, "Teenagers ages 13 to 17 are by far the most prolific texters, sending 1742 messages a month" Mr. Williams, a high school statistics teacher, was skeptical about the claims in the article. So he collected data from his first-period statistics class on the number of text messages they had sent over the past 24 hours. Here are the data:

$$\begin{array}{rrrrrrrrrrrr} \hline 0 & 7 & 1 & 29 & 25 & 8 & 5 & 1 & 25 & 98 & 9 & 0 & 26 \\ 8 & 118 & 72 & 0 & 92 & 52 & 14 & 3 & 3 & 44 & 5 & 42 & \\ \hline \end{array}$$

Sunny was the student who sent 42 text messages. What is Sunny's percentile?