Question

1. In an Anatolian town, 175 people aged 40 and over were randomly selected, of which 54% (.54) were found to be obese. For the mass ratio of people belonging to the mentioned age group in this town if the confidence interval is found as P(0.466<?<0.614), what is the meaning level of the study? 2. A new vaccine has been developed to treat a major disease. 7 patients were randomly identified and vaccinated and it was determined that they recovered on average 5.428 days. Since the mass variance is known to be 4 days, establish a confidence interval for the mass average at 99% confidence level.

Answer 1

1.

In the given scenario we have to use test statistic corresponding to one sample proportion test.

Here,

Thus we observe that,

  [Using R-code 'pnorm(1.964152)-pnorm(-1.964152)']

Hence, with 95% confidence proportion of obese people in Anatolian town is (0.466, 0.614).

2.

We have sample values as well as value of population standard deviation (or variance). So, we have to use test statistic of one sample z-test.

Corresponding test statistic is given by

Here,

Sample size

Sample mean

Population variance

We know,

  [Using R-code 'qnorm(1-(1-0.99)/2)']

Hence, 99% confidence interval for mass average is (3.480856, 7.375144).