Raul Walker

2022-07-09

According to a very large poll in 2015, about 90% of homes in California had access to the internet. Market researchers wonder if that proportion is now higher, so they take a random sample of 200 homes in California and find that 196 have access to the internet. They want to use this sample data to test H0:p = 0.9 versus Ha:p > 0.9, where p is the proportion of California homes with internet access. Which conditions for performing this type of significance test have been met?

Choose all answers that apply.

I. The data is a random sample from the population of interest.

II. np ≥ 10 and n (1 - p) ≥ 10

III. Individual observations can be considered independent.

Choose all answers that apply.

I. The data is a random sample from the population of interest.

II. np ≥ 10 and n (1 - p) ≥ 10

III. Individual observations can be considered independent.

Asdrubali2r

Beginner2022-07-10Added 14 answers

All three condition conditions will apply

Cheking for (II) condition. That is

$np\ge 10\text{and}n(1-p)\ge 10\phantom{\rule{0ex}{0ex}}\text{Given}p=0.90\phantom{\rule{0ex}{0ex}}n=200\phantom{\rule{0ex}{0ex}}np=200(0.90)\phantom{\rule{0ex}{0ex}}180\phantom{\rule{0ex}{0ex}}10\phantom{\rule{0ex}{0ex}}n(1-p)=200(1-0.90)\phantom{\rule{0ex}{0ex}}=200(0.10)\phantom{\rule{0ex}{0ex}}=2010$

When data has random sampling, (I) and (III) condition will automatically met.

Cheking for (II) condition. That is

$np\ge 10\text{and}n(1-p)\ge 10\phantom{\rule{0ex}{0ex}}\text{Given}p=0.90\phantom{\rule{0ex}{0ex}}n=200\phantom{\rule{0ex}{0ex}}np=200(0.90)\phantom{\rule{0ex}{0ex}}180\phantom{\rule{0ex}{0ex}}10\phantom{\rule{0ex}{0ex}}n(1-p)=200(1-0.90)\phantom{\rule{0ex}{0ex}}=200(0.10)\phantom{\rule{0ex}{0ex}}=2010$

When data has random sampling, (I) and (III) condition will automatically met.

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