Would you please explain or at least place the formulas to answer these questions?

Thank you in advance. I am working on them too.

1.(20.01) A study of commuting times reports the travel times to work of a random sample of 1000 employed adults in Chicago.

The mean isx= 40.0 minutes and the standard deviation iss= 56.9 minutes.

What is the standard error of the mean?21.881.806.991.09

2.(20.05) What critical valuet* from Table C would you use for a confidence interval for the mean of the population in each of the following situations? (If you have access to software, you can use software to determine the critical values.)

Step 1:

A 95% confidence interval based onn= 12 observations.2.5211.3722.2011.812

3.(20.09) The one-sampletstatistic from a sample ofn= 5 observations for the two-sided test of

H₀:= 50

H_a: 50

has the valuet= 2.50.

Step 1:

What are the degrees of freedom fort?11674

4.(20.17) We prefer thetprocedures to thezprocedures for inference about a population mean because

zrequires that you know the population standard deviation.zcan be used only for large samples.zrequires that you can regard your data as an SRS from the population.5.(20.18) You are testingH₀:= 100 againstH_a:< 100 based on an SRS of 9 observations from a Normal population. The data givex= 98 ands= 3. The value of thetstatistic is

-6.-2.-98.6.(20.19) You are testingH₀:= 100 againstH_a:> 100 based on an SRS of 16 observations from a Normal population. Thetstatistic ist= 2.13. The degrees of freedom for this statistic are

16.17.15.7.(20.20) You are testingH₀:= 100 againstH_a:> 100 based on an SRS of 16 observations from a Normal population. Thetstatistic ist= 2.13. TheP-value for the statistic

is less than 0.01.falls between 0.05 and 0.10.falls between 0.01 and 0.05.8.(20.21) You have an SRS of six observations from a Normally distributed population. What critical value would you use to obtain an 80% confidence interval for the mean of the population?

2.015.1.440.1.476.9.(20.22) You are testingH₀:= 0 againstH_a: 0 based on an SRS of 6 observations from a Normal population. What values of thetstatistic are statistically significant at the= 0.001 level?

t< 5.893 ort> 5.893.t> 6.869t< 6.869 ort> 6.869.10.(20.23) Twenty-five adult citizens of the U.S. were asked to estimate the average income of all U.S. households. The mean estimate was= $45,000 ands =$15,000. (Note: the actual average household income at the time of the study was about $68,000.) Assume the 25 adults in the study can be considered an SRS from the population of all adult citizens of the U.S. A 95% confidence interval for the mean estimate of the average income of all U.S. households is

$39,120 to $50,880.$39,867 to $50,133.$38,808 to $51,192.11.(20.24) Twenty-five adult citizens of the U.S. were asked to estimate the average income of all U.S. households. The mean estimate was= $45,000 ands =$15,000. (Note: the actual average household income at the time of the study was about $68,000.) Assume the 25 adults in the study can be considered an SRS from the population of all adult citizens of the U.S. Which of the following would cause the most worry about the validity of a 95% confidence interval that you calculate using this information?

A stemplot of the data shows a mild right-skew.You do not know the population standard deviation .You notice that there is a clear outlier in the data.12.(20.25) Which of these settings doesnotallow use of a matched pairstprocedure?

You interview a sample of 225 unmarried male students and another sample of 225 unmarried female students and ask each about the average number of minutes each day they spend using social media.You interview both spouses in 400 married couples and ask each about the average number of minutes each day they spend using social media.You interview 100 female students in their freshman year and again in their senior year and ask each about the average number of minutes each day she spends using social media.13.(20.26) Because thetprocedures are robust, the most important condition for their safe use is that

the data can be regarded as an SRS from the population.the population standard deviationis known.the population distribution is exactly Normal.14.(20.29) The Trial Urban District Assessment (TUDA) is a government-sponsored study of student achievement in large urban school districts. TUDA gives a reading test scored from 0 to 500. A score of 243 is a "basic" reading level and a score of 281 is "proficient." Scores for a random sample of 1400 eighth-graders in Dallas hadx

x

= 248 with standard error 1.0.

Step 1:

We don't have the 1400 individual scores, but use of thetprocedures is surely safe. Why?Because the sample doesn't have outliers.Because use of thetprocedures is always safe.Because the sample size is very large.Because the data has a strong skew.

15.In a randomized comparative experiment on the effect of color on the performance of a cognitive task, researchers randomly divided 66 subjects (27 males and 39 females ranging in age from 17 to 25 years) into three groups. Participants were asked to solve a series of 6 anagrams. One group was presented with the anagrams on a blue screen; one group saw them on a red screen; and one group had a neutral screen. The time, in seconds, taken to solve the anagrams was recorded. The paper reporting the study givesx

=

x

=

11.69 ands=

s

=

4.36 for the times of the n= 24 members of the neutral group.(Give your answer to three decimal places.)

A 98 % confidence interval for the mean time in the population from which the subjects were recruited is fromtoseconds.

16.(18.29) The placebo effect is particularly strong in patients with Parkinson's disease. To understand the workings of the placebo effect, scientists measure activity at a key point in the brain when patients receive a placebo that they think is an active drug and also when no treatment is given. The same six patients are measured both with and without the placebo, at different times.

Step 1:

Explain why the proper procedure to compare the mean response to placebo with control (no treatment) is a matched pairsttest.The proper procedure is a matched pairsttest because the same six patients are measured both with and without the placebo at different times.The proper procedure is a matched pairsttest because the placebo effect is particularly strong in patients with Parkinson's disease.The proper procedure is a matched pairsttest because there are exactly two groups - placebo and no treatment.The proper procedure is a matched pairsttest because scientists measure activity at a key point in the brain.