14. A large city is contemplating a ban on smoking in public...

14. A large city is contemplating a ban on smoking in public spaces .The city council wants to institute such a ban only if more than 70% of the adults living in the city support it. To find out if such support exists the city manager randomly selects 150 of the adult residents in the city and asks them Whether or not they support the ban. Of the 150 citizens, 108 support the ban and 42 do not. Is there sufficient statistical evidence to conclude that the strong support for the bin is present among the city's residents?

Transcript

00:01 A city is contemplating a ban on smoking.

00:03 They'll initiate it if more than 70 % of adults support it.

00:06 We want to see if that's the case based on our sample data.

00:09 So let's perform a hypothesis test.

00:12 We need the null and alternative hypotheses.

00:15 Now the null always gets some kind of equal sign.

00:17 The alternative doesn't.

00:19 So the check of more than 70 % is going to be the alternative.

00:23 So i'm going to put p, population proportion, more than 70%.

00:27 Null will be the opposite of that.

00:29 It's not more than 70%.

00:31 Our sample size is 150, looking at the proportion who support the ban, which is 108 people.

00:40 Giving me a sample proportion of 108 over 150, 0 .72.

00:46 To perform a hypothesis test, we start by assuming the null hypothesis is true.

00:51 So, we'll pretend p is 0 .7.

00:55 If i write every sample of size 150, take the sample of size 150, take the sample of a hypothesis, we start by assuming the null hypothesis is true.

00:58 And plot them out, i'd get something approximately normal.

01:03 P hat follows normal distribution, its mean is p, its deviation, root p, 1 minus p over n.

01:11 So this is the central limit theorem, and now i want to know where my sample would fall on this curve.

01:17 Maybe it falls here.

01:19 It's above 0 .7, but that's not unreasonable here.

01:22 It's very plausible how a sample came from a population with p equal to 0 .7.

01:28 But if p hat is way up here, i would say if the null hypothesis is true, this is really unlikely.

01:35 Therefore, i don't think it's true.

01:38 The cutoff point where we say, okay, that's too unlikely, is called alpha, the level of significance.

01:44 We've not been given one here, so we'll use the kind of default of 5%.

01:49 I'm going to use the critical value method.

01:51 So this is a right -tailed test.

01:55 I want the cut -off point for the top 5 % of this curve.

02:00 If it's just one tail, it gets all of alpha to itself.

02:04 It's called z sub 0 .05, and i know this is 1 .6 .5.

02:10 You might have a table of these, if not use the inverse normal function to get this from software or your calculator...

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