stats pt 1

Shargrodosky, Curhan, Curhan, and Eavey(2010)studied whether hearing loss among teens has increased. The researchers compared a random sample of 2928 teens from a 1994 study to a random sample of 1771 teens from a 2006 study . In the 1994 study, 480 teens had hearing loss while in the 2006 study, 333 had hearing loss. The researchers are trying to estimate the difference in the two populations, $LaTeX: pi_{2006} - pi_{1994}$
$π_{2006} - π_{1994}$ . The researchers tested the hypotheses
$LaTeX: H_0: pi_{2006} - pi_{1994}=0 text{ vs } H_A: pi_{2006} - pi_{1994} neq 0$
$H_{0} : π_{2006} - π_{1994} = 0 vs H_{A} : π_{2006} - π_{1994} \neq 0$
They calculated a p-value=0.0343 and Z=2.12 and designated
$α = 0.05$ . Answer the following questions using this information.

Identify the explanatory and the response variable.

Group of answer choices

The explanatory variable is whether or not the individual had hearing loss. The response variable is the year that the teens are in.

The explanatory variable is the year that the teens are in. The response variable is whether or not the individual had hearing loss.

The explanatory variable is the year that the teens are in. The response variable is the number of individuals who had hearing loss.

The explanatory variable is the number of individuals who had hearing loss. The response variable is the year that the teens are in.

Flag this QuestionQuestion 210 pts

Select all of the following statements that are correct.

Group of answer choices

The researchers would reject LaTeX: H_0
$H_{0}$ .

The researchers can generalize their results to the population of all teens.

The evidence is weak against LaTeX: H_0
$H_{0}$ .

The study results are based on a biased sampling method.

The researchers can declare the results are statistically significant.

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A clinical study conducted in the early 1990s recruited 324 pregnant women who were HIV-positive. The researchers believe that the pregnant women taking AZT will have fewer babies born HIV-positive. Of the 164 women who were randomly assigned to use the experimental (at the time) drug AZT, 13 had HIV-positive babies. Of the 160 women who were randomly assigned to receive a placebo, 40 had HIV-positive babies. The data has been summarized in the following table. Use this information to answer the following questions.

	AZT mothers	Placebo mothers	ROW TOTAL
HIV-positive baby	13	40	53
not HIV-positive baby	151	120	271
COLUMN TOTAL	164	160	n = 321

Flag this QuestionQuestion 38 pts

Is this study an observational study or an experiment?

Group of answer choices

This is an observational study since the drug AZT or placebo was randomly assigned to the pregnant women.

This is an observational study because the mothers were randomly sampled from the population.

This is an experiment because the mothers were randomly sampled from the population.

This is an experiment since the drug AZT or placebo was randomly assigned to the pregnant women.

Flag this QuestionQuestion 46 pts

Identify all of the parameters for this study.

Group of answer choices

$LaTeX: pi_{AZT}$
$π_{A Z T}$ is the long-run proportion of HIV-positive babies born to women taking AZT. $LaTeX: pi_{Placebo}$
$π_{P l a c e b o}$ is the long-run proportion of HIV-positive babies born to women taking the placebo.

$LaTeX: pi_{HIV}$
$π_{H I V}$ is the long-run proportion of HIV-positive babies born . $LaTeX: pi_{non}$
$π_{n o n}$ is the long-run proportion of non-HIV-positive babies born.

$LaTeX: pi_{AZT}$
$π_{A Z T}$ is the long-run proportion of women taking AZT. $LaTeX: pi_{Placebo}$
$π_{P l a c e b o}$ is the long-run proportion of women taking the placebo.

Flag this QuestionQuestion 56 pts

Write out the null and alternative hypotheses for this study.

Group of answer choices

$LaTeX: H_0: pi_{Placebo}-pi_{AZT} = 0 text{ vs } H_A:pi_{Placebo}-pi_{AZT} neq 0$
$H_{0} : π_{P l a c e b o} - π_{A Z T} = 0 vs H_{A} : π_{P l a c e b o} - π_{A Z T} \neq 0$

$LaTeX: H_0: pi_{Placebo}-pi_{AZT} = 0 text{ vs } H_A:pi_{Placebo}-pi_{AZT} < 0$
$H_{0} : π_{P l a c e b o} - π_{A Z T} = 0 vs H_{A} : π_{P l a c e b o} - π_{A Z T} < 0$

$LaTeX: H_0: pi_{Placebo}-pi_{AZT} = 0 text{ vs } H_A:pi_{Placebo}-pi_{AZT} data-verified=$ 0 “>
$H_{0} : π_{P l a c e b o} - π_{A Z T} = 0 vs H_{A} : π_{P l a c e b o} - π_{A Z T} > 0$

Flag this QuestionQuestion 66 pts

Are the validity conditions satisfied for this study?

Group of answer choices

No, there are not enough successes or failures.

Yes, the sample size was at least 20 and the sample data was not too strongly skewed.

Yes, there are at least 10 successes and 10 failures for each category of the explanatory variable..

No, the data was too strongly skewed.

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A random selection of married couples from Joliet, IL were asked to state how much TV they watched in the week of June 2 to June 8, 2019. The researchers are trying to determine if there is any difference in the TV watching habits between married couples. A matched pairs design was used and for each couple the difference (Wife – Husband) was calculated for each couple. The sample summary statistics and boxplots of the data are presented below.

Flag this QuestionQuestion 76 pts

State the null and alternative hypotheses.

Group of answer choices

$LaTeX: H_0: mu_d = 0 text{ vs } H_A: mu_d data-verified=$ 0″>
$H_{0} : μ_{d} = 0 vs H_{A} : μ_{d} > 0$

$LaTeX: H_0: mu_{wives}-mu_{husbands} = 0 text{ vs } H_A: mu_{wives}-mu_{husbands} neq 0$
$H_{0} : μ_{w i v e s} - μ_{h u s b a n d s} = 0 vs H_{A} : μ_{w i v e s} - μ_{h u s b a n d s} \neq 0$

$LaTeX: H_0: mu_{wives}-mu_{husbands} = 0 text{ vs } H_A: mu_{wives}-mu_{husbands} data-verified=$ 0″>
$H_{0} : μ_{w i v e s} - μ_{h u s b a n d s} = 0 vs H_{A} : μ_{w i v e s} - μ_{h u s b a n d s} > 0$

$LaTeX: H_0: mu_d = 0 text{ vs } H_A: mu_d neq 0$
$H_{0} : μ_{d} = 0 vs H_{A} : μ_{d} \neq 0$

stats pt 1

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