1 the length of the skulls of 10 fossil skeletons of an...

1. The length of the skulls of 10 fossil skeletons of an extinct species of bird has a mean of 5.68 cm and a standard deviation of 0.29 cm. Assuming that such measurements are normally distributed. (a) Find a 95% lower confidence interval for the mean length of the skulls of this species of bird. (b) Construct a 95% confidence interval for the true variance of the skull length of the species of birds. (c) Based on (b), construct a 95% confidence interval for the true standard deviation of the skull length of the species of birds.

Transcript

00:01 Hi, i'm david and i'm here to help you answer your question.

00:03 Now let me bring up your question here.

00:06 In this question we're going to discuss about the comfort interval for the mean and the variance as well as the standard deviation.

00:13 Let me remind you that the confident interval for the mean, and now we have the small sample size with the unknown standard deviation.

00:27 We will use the x bar plus or minus t and minus 1.

00:32 Degree of freedom, n -fought over 2 times s over square of n.

00:38 And the complete interval for the sigma square, it will be the n minus 1 times s square over the kai square of the degree of freedom equal to the n minus 1.

00:58 And then we have the n -for over 2, and then we will have b3.

01:03 The sigma here, sigma square, and then we will have the n minus 1 n square over the kai square of the n minus 1 with the 1 minus and 4 over 2.

01:22 And the comfort interval for the sigma, which you need to turn the square root of everything for the computer interval for the sigma square.

01:31 And now in this question here we're given the mean it will equal the x bar equal to the 5 .68 and the s it will equal to 0 .29 and in the part i am the question we want to find the 95 % lower competitive for the mean so here 95 % means that we have to find this t and now we have the n equal to 10 here so t here will be m and soon will be the 9 degree of freedom and then the n -file over 2 will be 0 025 it will look up the t table so let me bring on the t table for you and then i will show you have to use the t table here let me put the table down here for you and let me make it small here and now look at the table we have to look at the row with the nine freedom and then we have the unfaq equal to zon 025 and therefore the t we're looking for it will be equal to the 2 .22 6 2.

02:49 Therefore we should be able to find the 95 % combo interval for the mean it will be the xbary 5 .68 plus and minus t unfound which will be the 2 .2 62 times s can be 0 .29 over the square of the 10.

03:09 If we compute it, we have the 5 .168 plus and minus.

03:15 Here we will have the 0 .209, 10 2 .2 .62, divide me square of 10.

03:24 And then we get equal to the 0 .21.

03:28 And if we use the minus, we should get the 5 .68.

03:36 Minus the answer can equal to the 5 .47.

03:41 It will use the plus 5 .68 plus 0 .21 can equal to the 5 .89...