Question

The sodium intake for a random sample of patients at a dietician's office has been recorded. We will test How S2300 versus Hyp> 2300 at the 10% level of significance. The sample standard deviation is 516.17. The parameter of interest is A. the proportion of patients in the sample with above average sodium intake at this dietician's office. B. the average sodium intake of the sample of patients at this dietician's office. the average sodium intake of all patients at this dietician's office, D. the proportion of all patients with above average sodium intake at this dietician's office, QUESTION 15 The sodium intake for a random sample of patients at a dietician's office has been recorded. We will test Ho: MS 2300 versus Hi > 2300 at the 10% level of significance. The sample standard deviation is 516.17. What is the probability of making a type I error?

Answer 1

Q.1

We are given sample standard deviation s = 516.17

We need to test

H0 : $\mu$ $\leq$ 2300      vs      H1 : $\mu$ > 2300

So , here we wish to test that weather average sodium intake of all patient is more than 2300 or not . For testing this we took a random samples of patient at this dieticiane's office .

Thus here $\mu$ represents average population mean or here average sodium intake of all patient .

Thus correct option is

option C. The average sodium intake of all patient at this dieticiane's office .

Q.15 ( second part ) What is probability of making type I error .

Now , The probability of a type I error is the level of significance of the test of hypothesis ,

i.e probability of making type I error is nothing but $\alpha$ . Since we are given 10% of level of significance thus ,

Probability of making type I error $\alpha$ = 0.10

{ Note that - here no option are given so we write type I error only in genrall form }

Now type I error occurs when one rejects the null hypothesis when it is true. So in these case type I error occurs when reject null hypothesis i.e H0 : $\mu$ $\leq$ 2300 and falslt claim that average sodium intake of all patient is more than 2300 , but actuall average sodium intake of all patient is less than 2300 .