Country food includes seals caribou whales ducks fish and...

Name: country food includes seals caribou whales ducks fish and berries and is an important part of the diet of the aboriginal people called inuits who inhabit inuit nunangat the northern region o 61124
Uploaded: 2022-05-12T05:46:39-08:00
Duration: 14 min 2 s
Channel: Maitreya E
Description: country food includes seals caribou whales ducks fish and berries and is an important part of the diet of the aboriginal people called inuits who inhabit inuit nunangat the northern region o 61124

Country food includes seals, caribou, whales, ducks, fish and berries and is an important part of the diet of the aboriginal people called Inuits who inhabit Inuit Nunangat, the northern region of what is now called Canada. A survey of Inuits in Inuit Nunangat reported that 3274 out of 5000 respondents said that at least half of the meat and fish that they eat is country food. Calculate the standard error for the proportion. Calculate the z-score for the problem. Locate and calculate the p-value for the given problem. Using a 5% alpha level, is this result significant?

Transcript

0:00 Hello everyone.

00:01 In this question, it is given that in a survey of 160 canadian adults, 770 say that the energy situation in canada is very or fairly serious.

00:15 Hence, in question one, we need to find the point estimate for the population proportion.

00:21 In question two, we need to construct a 95 percentage confidence interval for the population proportion.

00:29 Therefore, we need to calculate a, the critical value, b, the margin of error, c, the lower limit of the interval and d, the upper limit of the interval.

00:41 In question 3, we need to find the minimum sample size needed to estimate the population proportion at the 99 % confidence level in order to ensure that the estimate is accurate within 5 % of the population proportion.

00:58 Therefore, again we need to calculate a, the critical value, b, the margin of error, and c, the sample size.

01:09 Now recall that the point estimate of the population proportion is the sample proportion, where the sample proportion for any event a is given as p subscript a and this is equal to the number of samples for which a is true.

01:29 That is for which the event a occurs divided by the sample size n now for a hundred multiplied by one minus alpha percentage confidence interval which in short is denoted by c i for the population proportion p where alpha is the significance level it is given as follows here the lower limit of the confidence interval is given by p minus c subscript alpha divided by 2 multiplied by the square root of p multiplied by 1 minus p divided by n and the upper limit of the confidence interval is given by p plus c subscript alpha divided by 2 multiplied by the square root of p multiplied by 1 minus b divided by n n is the sample size.

02:31 Here, c subscript alpha divided by 2 is the critical value at the significance level alpha.

02:38 It is also denoted as the c score and can be obtained from the standard normal distribution table.

02:47 Now the margin of error, in short, denoted by m e, is equal to c subscript alpha divided by 2 multiplied by the square root of p multiplied by 1 minus p divided by n.

03:05 In terms of the margin of error, therefore, the lower limit of the confidence interval can be written as p minus m e and the upper limit of the confidence interval can be written as p plus m e.

03:20 Now in question 1, since it is given that among 160 canadian adults, 7, 7 ,000 ,000, 70 say that the energy situation in canada is very or fairly serious.

03:36 Therefore the sample size n is equal to one zero six zero and hence the point estimate for the population proportion this will be denoted as small p and this is equal to the sample proportion which is equal to 770 divided by one zero 60 and this is approximately equal to 0 .726 therefore this is the answer to question one now in question two a we need to construct a 95 percentage confidence interval for this population proportion.

04:46 So, for a 95 percentage confidence interval, first let us obtain the significance level and we can do this by equating hundred multiplied by 1 minus alpha equal to 95.

05:05 Or from here we obtain alpha is equal to 0 .05 or alpha divided by 2 this is equal to 0 .025.

05:21 Therefore, the critical value at the significance level alpha is equal to 0 .05, this is equal to c subscript alpha divided by 2 and in our problem this is equal to c subscript 0 .025.

05:45 So the c score at the value 0 .025 can be obtained from the standard normal distribution table and this gives us the value 1 .96.

06:00 Therefore this is the answer to question 2a.

06:04 Now in question 2b, we need to find the margin of error.

06:11 Recall the margin of error m .e is given by the formula c subscript alpha divided by 2 multiplied by the square root of e multiplied by 1 minus b divided by n.

06:31 Substituting the values of c -subscript alpha divided by 2 as 1 .96, the population proportion as 0 .726, and the sample size in as 1 .60, we obtain the marginal error as 1 .96 multiplied by the square root of 0 .726 multiplied by the square root of 0 .726 multiplied by.

07:01 1 minus 0 .726 that is 0 .274 divided by 1060.

07:12 If we do this calculation we shall obtain the marginal error as approximately 0 .0269...

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