Can you tell me if my answers true,and How can i obtain the confidence interval?
a)A samle of 10 students scored the following grades:
40,42,35,54,57,54,46,42,54,57
(i)Find the sample mean ,mode and median.
Sample mean:
Sample mode:
mode is the most frequently ocurring value:
grades frequency
40 0
42 2
35 0
54 3
57 2
46 0
In this example we have more than one modal (multimodal)
Mode=42,54,57
Median:
First we must arrange the numbers in increasing order.
35,40,42,42,46,54,54,54,57,57
Here the batch size is even,so we have 2 middle values:
First middle value occure at the position(n/2)=(10/2=5)
The first middle value is 46
second middle value occure at the position[(n/2) +1]=6
The second middle value is 54
Median =[(46+54)/2]=50
(ii)Compute the sample standard deviation
(iii)Find 90%and 95%confidence intervals for the scores
How can I get the confidence interval ..
Here the sample size is <25 (sample size=10)
I know how to obtain the confidence interval when the sample size >25
buthow to obtain the confidence interval when the sample size <25
(B)Suppose that the grades in a course are normally distributed with mean 69 and standard deviation 12.
(i)Determine the ranges in which 90%,95%,and 99% of grades lie.
Approximately 90%grades were between:
(µ -1.64 *σ) and (µ+1.64 *σ)
(69-1.64*12) and(69+1.64*12)
(69-19.68) and (69+19.68)
49.32 and 88.68
================================
Approximately 95%grades were between:
(µ -1.96*σ) and (µ+1.96*σ)
(69-1.96*12) and(69+1.96*12)
(69-23.52) and(69+23.52)
45.48 and 92.52
=================
Approximately 95%grades were between:
(µ -2.58*σ) and (µ+2.58*σ)
(69-2.58*12) and(69+2.58*12)
(69-30.96) and(69+30.96)
38.04 and 99.96
==============================
(ii)Write down the mean and the standard error of the mean of samples of size 144.
Since n>25
x=µ=69
(iii)Find a range of values within which the means of approximately 95% of sample of size 144 lie.
Thank you for alerting me .. I think that we must include the numbers that occure more than once
Can you help me in the following point
(iii)Find 90%and 95%confidence intervals for the scores
How can I get the confidence interval ..
Here the sample size is <25 (sample size=10)
I know how to obtain the confidence interval when the sample size >25
buthow to obtain the confidence interval when the sample size <25