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It鈥檚 about ME Explain how each of the following would affect the margin of error of a confidence interval, if all other things remained the same.

a. Increasing the confidence level

b. Quadrupling the sample size

t time When constructing confidence intervals for a population mean, we almost always use critical values from a t distribution rather than the standard Normal distribution.

a. When is it necessary to use a t critical value rather than a z critical value when constructing a confidence interval for a population means?

b. For a particular level of confidence, explain what happens to the t critical values as Page Number: 548 the degrees of freedom increase.

The Gallup Poll interviews 1600 people. Of these, 18% say that they jog regularly. The news report adds: 鈥淭he poll had a margin of error of plus or minus three percentage points at a 95% confidence level.鈥� You can safely conclude that

a. 95% of all Gallup Poll samples like this one give answers within 卤3% of the true population value.

b. the percent of the population who jog is certain to be between 15% and 21%.

c. 95% of the population jog between 15% and 21% of the time.

d. we can be 95% confident that the sample proportion is captured by the confidence interval.

e. if Gallup took many samples, 95% of them would find that 18% of the people in the sample jog.

A Census Bureau report on the income of Americans says that with 90% confidence the median income of all U.S. households in a recent year was$\backslash (57,005$with a margin of error of$\backslash )742$. Which of the following is the most appropriate conclusion?

a. $90\%$of all households had incomes in the interval$\backslash (57,005卤\backslash )742$

b. We can be sure that the median income for all households in the country lies in the interval $\backslash (57,005卤\backslash )742$

c. $90\%$ of the households in the sample interviewed by the Census Bureau had incomes in the interval $\backslash (57,005卤\backslash )742$

d. The Census Bureau got the result$\backslash (57,005卤\backslash )742$using a method that will capture the true median income$90\%$of the time when used repeatedly.

e. $90\%$ of all possible samples of this same size would result in a sample median that falls within $\backslash (742$of $\backslash )57,005$

The U.S. Forest Service is considering additional restrictions on the number of vehicles allowed to enter Yellowstone National Park. To assess public reaction, the service asks a random sample of 150 visitors if they favor the proposal, Of these, 89 say "Yes."

a. Construct and interpret a $99\%$confidence interval for the proportion of all visitors to Yellowstone who favor the restrictions.

b. Based on your work in part (a), is there convincing evidence that more than half of all visitors to Yellowstone National Park favor the proposal? Justify your answer.

A milk processor monitors the number of bacteria per milliliter in raw milk received at the factory. A random sample of $10$one-milliliter specimens of milk supplied by one producer gives the following data:

Construct and interpret a $90\%$ confidence interval for the population mean $渭$.

The weights (in pounds) of three adult males are$160$,$215$and$195$. What is the standard error of the mean for these data?

a. $190$

b. $27.84$

c. $22.73$

d. $16.07$

e.$13.13$

In preparing to construct a one-sample t interval for a population mean, suppose we are not sure if the population distribution is Normal. In which of the following circumstances would we not be safe constructing the interval based on an SRS of size$14$from the population?

a. A stemplot of the data is roughly bell-shaped.

b. A histogram of the data shows slight skewness.

c. A boxplot shows that the values above the median are much more variable than the values below the median.

d. The sample standard deviation is large.

e. The sample standard deviation is small.

Many television viewers express doubts about the validity of certain commercials. In an attempt to answer their critics, Timex Group USA wishes to estimate the true proportion p of all consumers who believe what is shown in Timex television commercials. What is the smallest number of consumers that Timex can survey to guarantee a margin of error of $0.05$or less at a $99\%$confidence level?

a. $550$

b. $600$

c. $650$

d. $700$

e. $750$

You want to compute a $90\%$confidence interval for the mean of a population with an unknown population standard deviation. The sample size is $30$. What critical value should you use for this interval?

a. $1.645$

b. $1.699$

c. $1.697$

d. $1.96$

e. $2.045$