STAT HW 9-11

We observe a sample proprotion p-hat = 0.3. If the standard deviation of the sampling distribution of p-hat is 0.04, what is the 95% confidence interval for p?

(0.22, 0.38)

The correlation coefficient, r, can be a number between _____ and _____

-1 and 1

When drawing a conclusion from a hypothesis test with a 0.05 level of significance, we would say that there is sufficient evidence to conclude the alternative hypothesis, Ha, if the p-value equals

0.04

I love sharks! In fact, before I became a statistician, I wanted to be a marine biologist specializing in shark research (I even went to school for it for a little while). Of particular interest to me were hammerheads and great whites. Great white sharks are big and hungry. The lengths of 44 great white sharks tagged near False Bay, South Africa had a mean of 15.6 ft with standard deviation 2.5 feet. Based on this sample, is there evidence that the mean length of great white sharks near False Bay are greater than 15 feet? Use a significance level, α = 0.10. What is the actual value for the p-value of this test?

0.0548

It has been claimed that 70% of the students attending a large state university are opposed to a plan to increase student fees in order to build new parking facilities. You believe that more than 70% of the students are opposed to this plan. In order to test your theory, you decide to put what I've taught you this semester to use by randomly surveying 50 students and asking them if they are in favor of or opposed to the university's plan. What is the actual p-value for this test? Note: Round answers to 4 decimal places and include a leading zero, i.e., 0.5267.

0.0668

It is believed that 5% of all people requesting travel brochures for transatlantic cruises actually take the cruise within 1 year of the request. An experienced travel agent believes this is wrong. Of 100 people requesting one of these brochures, only 3 have taken the cruise within 1 year. We want to test the travel agent's theory with a hypothesis test.

0.3682

Ice cream consumption was measured over 30 four-week periods from March 18, 1951 to July 11, 1953. The purpose of the study was to determine if ice cream consumption depends on the variables price, income, or temperature. For this HW question, we want to see if the temperature (temp) affects the ice cream consumption (IC). Attached is the output from the simple linear regression of temperature on ice cream consumption. What is the predicted ice cream consumption when it's 65 degrees?

0.4084

A grocery chain runs a prize game by giving each customer a ticket that may win a prize when a box is scratched. Attached is the probability distribution printed on the ticket for a customer who shops at the grocery chain one a week. What is the probability that the customer wins no money? Note: Give your answer rounded to 2 decimal places, with a leading zero (ex: 0.99).

0.74

Ice cream consumption was measured over 30 four-week periods from March 18, 1951 to July 11, 1953. The purpose of the study was to determine if ice cream consumption depends on the variables price, income, or temperature. For this HW question, we want to see if the temperature (temp) affects the ice cream consumption (IC). Attached is the output from the simple linear regression of temperature on ice cream consumption. What is the value of the correlation coefficient, r?

0.7756

A psychologist thinks that listening to Mozart helps people think. She gives subjects a set of puzzles and measure how many they solve in 5 minutes while listening to Mozart. From data on a very large number of simulations, the psychologist gets the attached probability model. What is the probability that a subject solves more than 1 puzzle? Note: Round your answer to 1 decimal place and include a leading zero, ex. 0.5.

0.8

You play a game with two possible outcomes. Outcome A has probability 0.4 and outcome B has probability 0.6. When outcome B occurs, you win $2.00; otherwise, you lose $1.00. What is your expected value for this game? Note: Round your answer to 2 decimal places. If the expected value is less than 1, include a zero before the decimal (i.e., if your expected value is 50 cents, write 0.50). Do NOT include the dollar sign ($) in your answer.

0.8

If the standard deviation for waiting times in a line is 5 minutes, the standard deviation for the averages of 30 randomly chosen waiting times is _____ minutes

0.91

Larry Bird made 90% of this free throws during his professional career. To simulate one free throw shot by Larry Bird, we could use a random digit where

1 - 9 = made, 0 = missed

It has been claimed that 70% of the students attending a large state university are opposed to a plan to increase student fees in order to build new parking facilities. You believe that more than 70% of the students are opposed to this plan. In order to test your theory, you decide to put what I've taught you this semester to use by randomly surveying 50 students and asking them if they are in favor of or opposed to the university's plan. What is the value of the test statistic?

1.5

A psychologist thinks that listening to Mozart helps people think. She gives subjects a set of puzzles and measure how many they solve in 5 minutes while listening to Mozart. From data on a very large number of simulations, the psychologist gets the attached probability model. How many puzzles to you expect to be solved in 5 minutes? Note: Round your answer to 1 decimal place , ex. 57.5.

2.3

Ice cream consumption was measured over 30 four-week periods from March 18, 1951 to July 11, 1953. The purpose of the study was to determine if ice cream consumption depends on the variables price, income, or temperature. For this HW question, we want to see if the temperature (temp) affects the ice cream consumption (IC). Attached is the output from the simple linear regression of temperature on ice cream consumption. What percentage of change in ice cream consumption can be explained by temperature?

60.16

China has approximately 1.2 billion residents. Marketers want to know which international brands these residents have heard of. A large study showed that 62% of all Chinese adults have heard of Coca-Cola. You want to simulate choosing 10 Chinese at random and asking each if he/she has heard of Coca-Cola. Use the correct assignment of digits and the random digits below to simulate the answers of 10 Chinese. Read across the row of random digits from left to right. How many of these 10 Chinese have heard of Coca-Cola? 19223 95034 05756 28713 96409 12531 42544 82853 Note: Give your answer as a whole number with no decimal (ex: 12).

7

A grocery chain runs a prize game by giving each customer a ticket that may win a prize when a box is scratched. Attached is the probability distribution printed on the ticket for a customer who shops at the grocery chain one a week. Calculate the expected value. Note: Round your answer to 2 decimal places and do not include a dollar ($) sign (ex: 12.75).

9.50

It has been claimed that 70% of the students attending a large state university are opposed to a plan to increase student fees in order to build new parking facilities. You believe that more than 70% of the students are opposed to this plan. In order to test your theory, you decide to put what I've taught you this semester to use by randomly surveying 50 students and asking them if they are in favor of or opposed to the university's plan. Choose the correct interpretation of your test results.

At the 0.05 level of significance, there is insufficient evidence that the true proportion of all students that are opposed to the university's plan to increase student fees in order to build new parking facilities is greater than 0.70.

I love sharks! In fact, before I became a statistician, I wanted to be a marine biologist specializing in shark research (I even went to school for it for a little while). Of particular interest to me were hammerheads and great whites. Great white sharks are big and hungry. The lengths of 44 great white sharks tagged near False Bay, South Africa had a mean of 15.6 ft with standard deviation 2.5 feet. Based on this sample, is there evidence that the mean length of great white sharks near False Bay are greater than 15 feet? Use a significance level, α = 0.10. Give the correct interpretation of the conclusion of this significance test.

At the 0.10 level of significance, there is sufficient evidence that the average length of great white sharks near False Bay is greater than 15 feet.

It has been claimed that 70% of the students attending a large state university are opposed to a plan to increase student fees in order to build new parking facilities. You believe that more than 70% of the students are opposed to this plan. In order to test your theory, you decide to put what I've taught you this semester to use by randomly surveying 50 students and asking them if they are in favor of or opposed to the university's plan. If you used a significance level of 0.05, what is your decision for this test?

Fail to Reject H0

It is believed that 5% of all people requesting travel brochures for transatlantic cruises actually take the cruise within 1 year of the request. An experienced travel agent believes this is wrong. Of 100 people requesting one of these brochures, only 3 have taken the cruise within 1 year. We want to test the travel agent's theory with a hypothesis test. Using a significance level of 0.05, we can conclude that we have sufficient evidence that the true proportion of people that request travel brochures for transatlantic cruises and actually take the cruise within 1 year of the request is less than 0.05.

False

I love sharks! In fact, before I became a statistician, I wanted to be a marine biologist specializing in shark research (I even went to school for it for a little while). Of particular interest to me were hammerheads and great whites. Great white sharks are big and hungry. The lengths of 44 great white sharks tagged near False Bay, South Africa had a mean of 15.6 ft with standard deviation 2.5 feet. Based on this sample, is there evidence that the mean length of great white sharks near False Bay are greater than 15 feet? Use a significance level, α = 0.10. State the null hypothesis.

H0: μ = 15

It has been claimed that 70% of the students attending a large state university are opposed to a plan to increase student fees in order to build new parking facilities. You believe that more than 70% of the students are opposed to this plan. In order to test your theory, you decide to put what I've taught you this semester to use by randomly surveying 50 students and asking them if they are in favor of or opposed to the university's plan. State the alternative hypothesis.

Ha: p > 0.70

I love sharks! In fact, before I became a statistician, I wanted to be a marine biologist specializing in shark research (I even went to school for it for a little while). Of particular interest to me were hammerheads and great whites. Great white sharks are big and hungry. The lengths of 44 great white sharks tagged near False Bay, South Africa had a mean of 15.6 ft with standard deviation 2.5 feet. Based on this sample, is there evidence that the mean length of great white sharks near False Bay are greater than 15 feet? Use a significance level, α = 0.10. State the alternative hypothesis.

Ha: μ > 15

It has been claimed that 70% of the students attending a large state university are opposed to a plan to increase student fees in order to build new parking facilities. You believe that more than 70% of the students are opposed to this plan. In order to test your theory, you decide to put what I've taught you this semester to use by randomly surveying 50 students and asking them if they are in favor of or opposed to the university's plan. State the null hypothesis.

Ho: p = 0.70

The drying time for two different types of paint were sampled. 95% confidence intervals for Paint A and Paint B were (2.1, 3.4) hours and (3.0, 4.0) hours, respectively. Is there evidence that there is a difference in the average drying time of the two paints?

No, because the intervals overlap.

A psychologist thinks that listening to Mozart helps people think. She gives subjects a set of puzzles and measure how many they solve in 5 minutes while listening to Mozart. According to the Law of Large Numbers ____________________________________.

Observe many subjects and record how many puzzles each solves. The average will be close to the expected value.

It has been claimed that 70% of the students attending a large state university are opposed to a plan to increase student fees in order to build new parking facilities. You believe that more than 70% of the students are opposed to this plan. In order to test your theory, you decide to put what I've taught you this semester to use by randomly surveying 50 students and asking them if they are in favor of or opposed to the university's plan. Which expression represents the p-value for this text?

P(p-hat > 0.80 | p = 0.70)

The probability that a sample statistic as extreme or more extreme as the one seen in our sample would arise just by chance is known as:

P-value

If we roll one die, which of the following events is mutually exclusive of rolling a 2?

Rolling an odd number.

This dataset contains the prices of ladies' diamond rings and the carat size of their diamond stones. The rings are made with gold of 20 carats purity and are each mounted with a single diamond stone. Attached are the results from the simple linear regression of diamond size on price. What is the explanatory variable?

diamond size

A strong relationship between two variables is always evidence that changes in one variable cause changes in the other.

false

You gather data on the number of hours of TV news broadcasts watched per week and the grade point average (GPA) of juniors majoring in journalism. You expect that TV news broadcast watching will help explain grades. In a scatterplot of your data,

hours of TV news broadcast watching should be on the horizontal axis.

Ice cream consumption was measured over 30 four-week periods from March 18, 1951 to July 11, 1953. The purpose of the study was to determine if ice cream consumption depends on the variables price, income, or temperature. For this HW question, we want to see if the temperature (temp) affects the ice cream consumption (IC). What is the response variable?

ice cream consumption

Ice cream consumption was measured over 30 four-week periods from March 18, 1951 to July 11, 1953. The purpose of the study was to determine if ice cream consumption depends on the variables price, income, or temperature. For this HW question, we want to see if the temperature (temp) affects the ice cream consumption (IC). Attached is the output from the simple linear regression of temperature on ice cream consumption. For every one degree increase in temperature, we expect ice cream consumption to __________.

increase by 0.0031 pints per capita

When knowledge of the outcome of one event gives no information about the outcome of another event, we say that the two events are

independent

If the alternative hypothesis, Ha, for a test is p < 0.5, we have a/an

lower tail test

NFL quarterbacks earn more (on the average) than running backs, who in turn earn more than linemen. The correlation coefficient r between a player's salary and his position

makes no sense.

A recent Gallup Poll interviewed a random sample of 1,523 adults. Of these, 868 bought a lottery ticket in the past year. Suppose that, in fact, (unknown to Gallup) exactly 60% of all adults bought a lottery ticket in the past year. If Gallup took many SRSs of 1,523 adults, the sample proportion who bought a ticket would vary from sample to sample. The sampling distribution would be close to normal with

mean 0.6 and standard deviation 0.0126

It is believed that 5% of all people requesting travel brochures for transatlantic cruises actually take the cruise within 1 year of the request. An experienced travel agent believes this is wrong. Of 100 people requesting one of these brochures, only 3 have taken the cruise within 1 year. We want to test the travel agent's theory with a hypothesis test. p = 0.05 is the _________.

null hypothesis, H0, for this test.

It has been claimed that 70% of the students attending a large state university are opposed to a plan to increase student fees in order to build new parking facilities. You believe that more than 70% of the students are opposed to this plan. In order to test your theory, you decide to put what I've taught you this semester to use by randomly surveying 50 students and asking them if they are in favor of or opposed to the university's plan. If 40 people in your sample say they are opposed to the extra fees, give a point estimate for the proportion of students opposed to the extra fees.

p-hat = 0.80

This dataset contains the prices of ladies' diamond rings and the carat size of their diamond stones. The rings are made with gold of 20 carats purity and are each mounted with a single diamond stone. Attached are the results from the simple linear regression of diamond size on price. What is the direction of the relationship between these two variables?

positive

This dataset contains the prices of ladies' diamond rings and the carat size of their diamond stones. The rings are made with gold of 20 carats purity and are each mounted with a single diamond stone. Attached are the results from the simple linear regression of diamond size on price. What is the response variable?

price

You gather data on the number of hours of TV news broadcasts watched per week and the grade point average (GPA) of juniors majoring in journalism. You expect that TV news broadcast watching will help explain grades. The plot of the data shows that students who watch more TV news broadcasts tend to have higher GPAs. A plausible value for the correlation r between hours of TV and GPA is

r = 0.4.

The name for the pattern of values that a statistic takes when we sample repeatedly from the same population is the

sampling distribution of the statistic

The _____________ tells us what fraction of the variation in the response variable is explained by the straight-line correlation between x and y.

squared correlation, r2

The correlation between the heights of fathers and the heights of their adult sons is r = 0.52. This tells us that

taller than average fathers tend to have taller than average sons.

Ice cream consumption was measured over 30 four-week periods from March 18, 1951 to July 11, 1953. The purpose of the study was to determine if ice cream consumption depends on the variables price, income, or temperature. For this HW question, we want to see if the temperature (temp) affects the ice cream consumption (IC). What is the explanatory variable?

temperature

In a statistical test of hypotheses, we say the data are statistically significant at level α if

the P-value is less than α.

In a scatterplot we can see

the form, direction, and strength of a relationship between two quantitative variables.

The P-value of a test of significance is calculated assuming

the null hypothesis is true

If the P-value of a test of significance is 0.999 then

the null hypothesis provides a plausible explanation of the data.

For a given level of confidence, increasing the sample size will decrease the width of the confidence interval

true

For a given sample size, increasing the level of confidence will increase the width of the confidence interval

true

In statistical language, a "95% confidence interval" means that we used a method that captures the true value of the parameter 95% of the time

true

Significance tests are designed to assess the strength of the evidence against the null hypothesis

true

The intercept is the value of y when x = 0

true

The least-squares regression line of y on x is the line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible.

true

China has approximately 1.2 billion residents. Marketers want to know which international brands these residents have heard of. A large study showed that 62% of all Chinese adults have heard of Coca-Cola. You want to simulate choosing 10 Chinese at random and asking each if he/she has heard of Coca-Cola. One correct way to assign random digits to simulate the answer is:

two digits simulate one person's answer: 00 - 61 mean "yes" and 62 - 99 mean "no"

The correlation between the heights of fathers and the heights of their adult sons is r = 0.52. If the heights were first measured in feet (one foot equals 12 inches), and later measured in furlongs (one furlong equals 7,920 inches), the correlation between heights of fathers and heights of sons would be

unchanged: equal to 0.52.