Question

1. A population forms a normal distribution with a mean of µ = 120 and a standard deviation of σ = 14.

1. If two scores were selected from this population, how much distance would you expect, on average, between the second score and the population mean?
2. A sample of n = 20 scores from this population has a mean of M = 90, do you think this sample is relative typical or extreme to the population? Explain.
3. With a large standard deviation in a population, will the scores be central or spread out?

Answer 1

a) Population mean µ = 120, Std Dev σ = 14, Mean is the average values or the middle value and Standard deviation  is how far the data points deviates from the middle or Mean. Hence If two scores were selected from this  population, the distance between the second score and the population mean is 14 which is the σ.

b) Null Hypothesis H0 µ = 120

Alternate hypothesis H1 µ not= 120

We will use alpha as 0.05 for this example. As this is a two-tailed test, split the alpha into two.
0.05/2=0.025.Hence the t value for n-1=19 and alpha=0.05 is 2.09.

The test statistic is calculated as:

,

t=(120-90)/$\sqrt{}$142 /20

t=9.584

Here the test statistics 9.584 is gerater than 2.09.Hence we can reject the null hypothesis saying that the sample is extreme to the population.

c) With a large standard deviation in a population,the scores are highly deviated from the central and spread out.Because higher the standard deviation lesser points towards the cenral.