Question

- The
*General Social Survey*recently asked 1,294 randomly selected Americans whether they performed any volunteer work during the past year. A total of 617 people said they did. A sociologist states that half of all Americans perform volunteer work in a given year. Test the hypothesis that less than half of all Americans perform volunteer work. Use a significance level of 5%.

- State the null and alternative hypotheses [4]

- Check the assumptions [3]

- Give the test statistic [2]

- Give the P-value and the conclusion reached about the null hypothesis based on the P-value [2]

- Summarize the final conclusion in the context of the claim [2]

- Construct the corresponding confidence interval [3]

- Find the margin of error for confidence interval above [2]

Answer #1

Between September 25 and 28 of 2014, the Pew Research Center
asked 101 randomly selected Americans the following question: On
which of these activities does the US government currently spend
the most money? Is it Social Security, transportation, foreign aid,
or interest on the national debt?
20 people said Social Security (the correct answer), while 4 said
transportation, 33 said foreign aid, and 26 said interest. 18 said
they don’t know or refused to answer.
Remember for a Bernoulli variable...

The General Social Survey was completed for a simple
random sample of 977 adult Americans in 2004. One of the questions
asked: “In general, how do you feel about your time—would you say
that you always feel rushed even to do things you only have to do,
only sometimes feel rushed, or almost never feel rushed?” 31.1% of
respondents reported that they “always” feel rushed.
Researchers claim that one-third of all Americans would
answer “always.” Test this claim at a...

Suppose a coin is randomly tossed n = 400 times, resulting in X
= 240 Heads. Answer each of the following; show all work!
(a) Calculate the point estimate, and the corresponding
two-sided 95% confidence interval, for the true probability pi =
P(Heads), based on this sample.
(b) Calculate the two-sided 95% acceptance region for the null
hypothesis H0: pi = 0.5 that the coin is fair.
(c) Calculate the two-sided p-value (without correction term) of
this sample, under the...

A sample survey asked a random sample of 1498 adult Canadians,
“Do you agree or disagree that all firearms should be registered?”
Of the 1498 people in the sample, 1282 answered either “Agree
strongly” or “Agree somewhat.” Assuming this survey can be
considered an SRS of all adult Canadians, what is the proportion of
all Canadians who agree (as described) that all firearms should be
registered?
Your solution must include the following parts, in order. Point
form is fine.
a)...

The report "Digital Democracy Survey"† describes a large
national survey. In a representative sample of Americans ages 14 to
18 years, 45% indicated that they usually use social media while
watching TV. Suppose that the sample size was 500. (a) Is there
convincing evidence that less than half of Americans ages 14 to 18
years usually use social media while watching TV? Use a
significance level of 0.05. State the appropriate null and
alternative hypotheses. H0: p = 0.5 versus...

#1. A survey organization recently conducted a random sample of
1000 individuals from the population of American adults. The survey
assessed the relationship between religiosity and partisanship. It
asked the individuals whether religion is an important part of your
life,” and asked them if they think of themselves as Democrats,
Republicans, or Independents. The results were as follows:
Partisanship
Religion Not Important
Religion Important
Total
Democrat
130
220
350
Independent
85
255
340
Republican
35
275
310
Total
250
750...

From a random sample of 780 US homes it was found that 655 had
broadband Internet access. Construct a 95% confidence interval for
the proportion of US homes with broadband Internet access.
Technology results for this problem:
Give the null and alternative hypotheses; (2 points)
Is this a one‐tailed or two‐tailed test? Think about the null
hypothesis. How do you know
that this is a one or two‐tailed test? (1 point)
Show whether the criteria for approximate normality are met....

Question 4:
An article in Wikipedia claims that the mean body
temperature of adults is less than 98.6° F. This goes against
everything you’ve ever been taught, so you gather 565 healthy
adults and observe a mean body temperature of 98.2°F, with the
sample standard deviation of 2.6°F. Test the article’s claim at a
5% level of significance.
If the problem is a confidence interval:
Show whether the criteria for approximate normality are
met. (1 point)
Summarize the sample statistics....

1. A Gallup poll asked 1200 randomly chosen
adults what they think the ideal number of children for a family
is. Of this sample, 53% stated that they thought 2 children is the
ideal number. Construct and interpret a 95% confidence interval for
the proportion of all US adults that think 2 children is the ideal
number.
2. There were 2430 Major League Baseball games
played in 2009, and the home team won the game in 53% of the games....

6) The Family and Medical Leave Act provides job
protection and unpaid time off from work for a serious illness or
birth of a child. In 2000, 60% of respondents of a survey stated
that it was very easy to get time off for these circumstances. A
researcher wishes to see if the percentage who said it was easy to
get time off has changed. A sample of 100 people who used the FMLA
revealed that 56% found it easy...

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