00:01
So over the past few decades, public health officials have examined the link between weights, concerns and teenage girls smoking.
00:08
Researchers surveyed a group of 273 randomly selected teen eight girls living in massachusetts between 12 and 15 years old after four years.
00:19
The girls are surveyed again and 63 of them said they smoke to stay thin.
00:23
Is there a good evidence that more than 30 % of the teen girls smoke to stay thin? so we are to assume a 5 % level of significance.
00:33
So let's go into our worksheet and extract out all of the message details.
00:37
So our sample size n is actually cost to 273.
00:41
We have the fraction of the sample.
00:43
We have that to be equals to 63 rather.
00:50
And then that means our sample proportion pickup is going to be 63 divided by 273.
00:56
And when we'll do the match, 63 divided by 273.
00:59
We have that to be cost to 0 .23 and our sample proportion p is actually equals to 30 percent so the sum the population proportion radar is actually equals to 30 percent and the sample proportion is 0 .23 which can be rewritten as 23 percent so our question says that is there good evidence that more than 30 percent of the teenage girls smoke to state team so after uh extracting all of our details the next step is first to state the null and alternative hypothesis so our h not is based on the fact that p is greater than or equals to 30 percent and the alternative hypothesis is that p is less than 30 percent so after stating the null and alternative hypothesis the next step is for us to get the test statistics which can either be a z test or e t test so there is a condition that allows us to use a normal discretion to model a proper question and that is an np n p cap rather than or equals to 5 and nq carp must be greater than no equals to 5 so our n in this case of answers to 173 our pickup is 0 .23 so let's try that np cap is going to be cost to 273 times 0 .23 and when we do the mat 273 times 0 .23 we have our answer to be 62 .79 and nq cap is equal to 273 times so 1 minus 0 .23 that gives us 0 .77 so 273 times 0 .77 that gives us 210 .21 as you can see both values right here are actually greater than 5 so it simply implies that we've satisfied the condition that will allow us to use a normal distribution to model our question so what i got to do you so we've satisfied the condition that allows us to use a normal distribution to approximate our data sets so our test statistics is it as given to us as by the square root of p times q divided by n our pick up in this case of ours is actually 0 .23 minus our p is our 0 .30 divided by the square root of so p is our 0 .30 times q is going to be 1 minus 0 .30 which is 0 .70 divided by 273 so 0 .23 so 0 .23 minus 0 .30 so using our calculator to work on everything we have at the denominator, we have the square root of 0 .30 times 0 .70 divided by 273 and that gives us 0 .077...