In a random sample of 120 people 54 had suffered moderate to...

In a random sample of 120 people, 54 had suffered moderate to severe damage to their voices. a) For any $\alpha \in (0,1)$, what can we assert about the maximum error of using the sample proportion $\hat{\theta} = x/n$ as an estimate of the true proportion $\theta$ with $(1-\alpha)\%$ confidence? b) With 90% confidence, what can we say about the maximum error if we used the sample proportion $\frac{54}{120} = 0.45$ as an estimate of the true proportion that suffered moderate to severe damage to their voices?

Transcript

00:01 Hello everyone.

00:02 In the 21st question, if you see n value is 100, x is 12.

00:13 So the point estimate is point estimate is equal to x divided by n which is 12 divided by 100.

00:28 0 .12 is the answer.

00:34 Now in the question number 22, margin of error.

00:39 Is 4 % which is 0 .04 and 95 % confidence interval has significance level 0 .05.

00:52 So the critical value z alpha divided by 2 is equal to 1 .96.

00:59 Now we need to find the sample size n which is n is equals to z alpha divided by 2 divided by 4 e whole square so this is 1 .96 divided by 4 multiplied by 0 .04 whole square and this answer is approximately 601 this is the sample size now in 23rd it is given that n is equal to 435 and x is equal to 120 the point estimate will be x divided by n which is 120 divided by 435 and we will get the answer 0 .276 so this is the answer for the 23rd in the 24th it is given that sample size is 4 .76 so this is the answer for the 23rd in the 24th it is given that sample size is 4.

02:19 Sample mean is 23 .8 standard deviation is 4 .3.

02:26 Now the null hypothesis is if mu is equal to 22 and the alternative hypothesis is if mu is greater than 22.

02:38 Now we need to find out the test statistic t is equals to x bar minus mu divided by s divided by under root in and this is 23 .8 minus 22 divided by 2 .3 divided by under root 40.

03:00 So if we calculated we'll get the test statistic 2 .67...

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