00:01
In a sample of 1 ,000 people, it was found that 540 are rice eaters and the rest are wheat eaters.
00:07
And we were asked, can we assume that both rice and wheat are equally popular at the 1 % level of significance? so here's what the hypotheses are.
00:19
The null hypothesis here is that the population proportion of people who are rice eaters is the same as those who are wheat eaters, so 0 .5.
00:31
And the alternative hypothesis is that this proportion is something different from 0 .5.
00:42
We want to test these hypotheses at a 1 % level of significance, so that's alpha equals 0 .01.
00:51
Because this is a large sample proportion, we can calculate a test statistic from the standard normal distribution.
00:57
It's calculated as the sample proportion minus the null hypothesized proportion divided by the square root of the null proportion times the one minus the null proportion over the sample size.
01:13
So first let's calculate the sample proportion, that's 540 out of 1000, and that's approximately point, well that's exactly .54.
01:29
And so we calculate the test statistic as follows, and this comes out to approximately 2 .530...