Question

For the following example:

a) Confirm that the work provided is correct OR provide guidance on corrections that are needed.

b) For the 99% confidence interval, provide a hypothesis test decision and explain your reasoning.

c) For the effect size, interpret the obtained value (not using the size).

d) Explain why effect size is needed in addition to results of a hypothesis test.

EXAMPLE:

a) You are investigating how the number of pairs of pointe shoes bought per year differs based on a ballerina's age. The population mean for all ballerinas at one studio was 14, and the standard deviation was 4. A sample of 20 randomly selected ballerinas from the studio over the age of 18 had a mean of 16.

b) The example is appropriate because it is comparing the mean number of pointe shoes bought by a single sample of ballerinas to the mean number bought by the studio population.

c) s_M= ??√=420√=0.894sN=420=0.894

df= 20-1= 19

Critical values for 2-tailed test with p=0.01 and df= 19 --> -2.861 and +2.861

M_lower= −?(??)+???????=−2.861(0.894)+16=13.44−t(sM)+Msample=−2.861(0.894)+16=13.44

M_higher= ?(??)+???????=2.861(0.894)+16=18.56t(sM)+Msample=2.861(0.894)+16=18.56

So, the 99% confidence interval is [13.44,

18.56]

?(13.44≤?≤18.56)=0.99p(13.44≤μ≤18.56)=0.99

Effect Size

Cohen's d= (???????−?)?=(16−14)4=0.5(Msample−μ)s=(16−14)4=0.5

So, the effect size is medium

Answer 1

Given:

Sample mean = x̄ = 16

Sample size = n = 20

Population standard deviation = = 4

Population mean = = 14

Hypothesis test:

The null and alternative hypothesis is

Ho : = 14

Ha : 14

Since population standard deviation is known, we use z distribution.

Which is the required solution.