3 body length of deer mice is normally distributed with mean...

Name: 3 body length of deer mice is normally distributed with mean mu unknown consider a random sample of 14 deer mice with sample mean of body length 911 mm and standard deviation 8 mm 1 find the 74368
Uploaded: 2023-12-12T01:12:24-08:00
Duration: 3 min 57 s
Channel: Joanna Quigley
Description: 3 body length of deer mice is normally distributed with mean mu unknown consider a random sample of 14 deer mice with sample mean of body length 911 mm and standard deviation 8 mm 1 find the 74368

3. Body length of deer mice is normally distributed with mean $\mu$ (unknown). Consider a random sample of 14 deer mice with sample mean of body length 91.1 mm and standard deviation 8 mm. 1. Find the sampling distribution of the sample mean? Since $X \sim N$, but $\sigma_x$ is unknown, $\bar{X} \sim t_{13}$

Transcript

00:01 So we're looking at the length of deer mice, and this is a normal distribution with a mean of 83 mm and a standard deviation of 7.

00:11 And we're looking at samples of 25.

00:15 So i'm going to refer to the central limit theorem, which states that as sample size increases, sample means become more and more normally distributed compared to the population.

00:26 Since we have a normal population here, and you can't get more normal than normal, if i took every sample of this size, took the sample means and plotted them out, i would just get another normal distribution.

00:39 The mean of the means is the same as the population mean, so 83.

00:45 The standard deviation of the sample means, or standard error, is sigma over root n.

00:53 So 7 over 5 is 1 .4.

00:55 So i have the original distribution and the sampling distribution, which is narrower.

01:06 So there's a depiction of them.

01:09 Part c.

01:12 We want to look at a length, so that 10 % of all deer mice have a length below this.

01:18 So we're looking at individuals, and there's going to be some value where 10 % of them are below that.

01:24 So that's the 10th percentile for the population.

01:28 To find this, you need something with the normal distribution built into it.

01:34 That could be software like excel.

01:36 I'm going to use my ti -84 calculator with the inverse normal function.

01:43 It has three inputs.

01:45 Area, mean, standard deviation.

01:47 I put in the cumulative area, so here that would be 10%, or 0 .1, with the mean and standard deviation.

01:53 We're looking at all mice, so i put 7 there.

01:58 And that gives me 74 .03, to two decimal places.

02:03 That's in millimetres.

02:05 Part 4...

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