Question

A 2020 Pew Research survey asked a random sample of 4860 American adults if they have ever used online dating (website or mobile app) and found that 30 percent of respondents had ever done so.

Q1

Which math symbol(s) would represent the cited value 30 percent?

mm

nn

x¯x¯

x¯1−x¯2x¯1−x¯2

σσ

CC

zz

μdiffμdiff

μμ

tt

p^p^

x¯diffx¯diff

μ1−μ2μ1−μ2

Q2

(Please answer very clear and detail)

Obtain a 95% confidence interval estimating the prevalence (rate) of online dating among American adults as of 2020. Interpret this interval in context (be sure to be explicit and to cite the values of the CI).

[This question will be graded manually]

Q3

Which inference procedure should be used to obtain this confidence interval?

a.) ANOVA for several means

b.) one sample or matched-pairs t procedure for a mean

c.) chi-square for two-way tables

d.) z procedure for a proportion

e.) two sample t procedure for two means

Q4

What are the conditions for this confidence interval?

a.) One random sample AND large enough counts of successes and failures in the sample.

b.) Independent random samples AND normal data or large enough total sample size.

c.) Independent random samples AND normal data AND large enough total sample size AND similar sample standard deviations.

d.) One random sample AND normal data AND large enough sample size.

e.)Random selection without repeated measures AND large enough expected counts.

f.) Independent random samples AND normal data AND large enough total sample size.

g.) Independent random samples AND normal data or large enough total sample size AND similar sample standard deviations.

h.) One random sample AND normal data or large enough sample size.

i.) Normal data AND large enough expected counts.

Answer 1

1) the math symbol that will be used for the cited value 30 percent?

Answer: p^

2) 95% confidence interval:

Following formula can be used to calculate the confidence interval:

Given values:

p = 0.3

n = 4860

z = 1.96 ( at given 95% confidence interval)

Putting the values in the formula we get:

We are 95% confident that the proportion of correspondents who have used the dating site is between 0.2872 and 0.3128

3)

Which inference procedure should be used to obtain this confidence interval?

a.) ANOVA for several means

b.) one sample or matched-pairs t procedure for a mean

c.) chi-square for two-way tables

d.) z procedure for a proportion

e.) two-sample t procedure for two means

4)

What are the conditions for this confidence interval?

a.) One random sample AND large enough counts of successes and failures in the sample.

b.) Independent random samples AND normal data or large enough total sample size.

c.) Independent random samples AND normal data AND large enough total sample size AND similar sample standard deviations.

d.) One random sample AND normal data AND large enough sample size.

e.)Random selection without repeated measures AND large enough expected counts.

f.) Independent random samples AND normal data AND large enough total sample size.

g.) Independent random samples AND normal data or large enough total sample size AND similar sample standard deviations.

h.) One random sample AND normal data or large enough sample size.

i.) Normal data AND large enough expected counts.