The legal limit for blood alcohol is 0.08%. A person makes...

The legal limit for blood alcohol is 0.08%. A person makes four measurements using one breathalyzer and obtains the following results: X? = 0.080 X? = 0.085 X? = 0.085 X? = 0.079 X??? = 0.0823 It this person above the legal limit within a 95% confidence limit? A) Determine with a well characterized ? = 0.003 B) Determine with an unknown standard deviation.

Transcript

00:01 In this question, the legal limit is given for drinking for blood alcohol that is 0 .08 % and the results are given we have to determine with a well characterized sigma equals to 0 .0 .0.

00:15 So first of all, we will have the given data.

00:18 So we have sigma of x squared that is equals to 0 .027.

00:22 So sigma of x that is equals to 0 .329 and the n is equal to 4.

00:28 So here the x bar, the mean is 0 .329 divided by 4, which is equal to 0 .08.

00:35 So this is the x bar here.

00:37 So if we calculate the variance x squared, that is 1 divided by n minus 1 multiplied by sigma x square minus sigma x squared minus sigma x squared divided by x.

00:47 So putting these values over there.

00:49 So 1 divided by 3, this is 0 .027 minus this is 0 .329 whole square divided by 4.

00:57 So solving this value we get 1 divided by 3 multiplied by 0 .003075.

01:06 So solving it out, we get this value of s that is equal to, s square is equals to 1, that is 0 .000015.

01:16 So what is the variance here? so s, the standard deviation is given by root of 0 .00000025, which is equal to 0 .000015.

01:27 So this is the value of l.

01:30 Now in the a part we have the sigma is equals to 0 .03.

01:36 And if we check for the hypothesis here, so h0 is such that u is equal to 0 .08, an alternate hypothesis is is not equal is greater than, it is greater than 0 .0.

01:49 So we have to calculate the test status...

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