SOLUTION: The government of a wealthy country intends to institute a program to discourage investment in foreign countries by its citizens. It is known that in the past 35% of the country�

Question 1179727: The government of a wealthy country intends to institute a program to discourage investment in foreign countries by its citizens. It is known that in the past 35% of the country’s adult citizens held investment in foreign countries. The government wishes to determine if the current percentage of adult citizens, who own foreign investment is greater than this long term figure of 35%. A random sample of 800 adults is selected and it is found that 320 of these citizens hold foreign assets. Is this percentage greater than 35%. Use a 10% significance level for testing this claim.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
at 10% significant level, the one-tailed critical z-score is 1.28155 rounded to 5 decimal places.

we use a one tailed critical z-score because we are testing whether the sample men is greater than the assumed population mean.

if we were testing whether the sample mean was not equal to the assumed population mean, then we would have used a two tailed critical z-score.
in that case, the critical z-score would have been 1.64485 rounded to 5 decimal places.

the z-score formula is:

z = (x - m) / s

x is the raw score.
m is the mean.
s is the standard error.

with a ratio problem like this, you get:

p0 = .35
1 - p0 = .65
ph = 320/800 = .4

p0 is the assumed population proportion.
ph is the sample proportion.

in the reference ph is equal to p-hat.
that's a p with a ^ on top of it.
it looks like the letter p is wearing a hat.
i can't draw it, but you can see what it looks like in the reference.

with a ratio problem, such as this, the z-score formula of:

z = (x - m) / s

becomes:

z = (ph - p0) / s

the value of s is equal to sqrt(p0 * (1 - p0) / n)

in this problem, that becomes:

s = sqrt(.35 * .65 / 800) = .016863422.

the z-score becomes:

z = (.4 - .35) / .016863422 = 2.96500 rounded to 5 decimal places.

since that is greater than the critical z-score of 1.64485, the results are considered significant and the conclusion is that the percentage of adult citizens who own foreign investment is more than likely greater than 35%.

here's the reference.

https://online.stat.psu.edu/statprogram/reviews/statistical-concepts/proportions

there are lots of reference on the internet.
this one was the easiest to understand, at least for me.

note that the critical z-score has an area under the normal distribution curve of .10 to the right of it.

not that oue test z-score has an area under the normal distribution curve of .0015 to the right of it.

that's significantly less than .10, so the conclusion is the same.
the results are significant and he conclusion is that the percentage is more then likely greater than 35%.

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