Question

1. You are interested in developing a software program targeted at learning a new foreign language. You believe that your new program will allow for faster language learning in adults. Typically, it takes people an average of 5 years (σ = 0.76) to learn a second language. In your sample of 30 adults, this same level of proficiency is achieved in 2.8 years (S = 0.78). (Assume the standard α = 0.05.)

Population 1 (1):

Population 2 (1):

Create a graphical representation of your two distributions (Please include both distributions on the same graph and label the means on your x axis) (2):

Null hypothesis (in symbol format) (1):

Research hypothesis (in symbol format) (1):

Independent Variable (1):

Dependent Variable (1):

What is your probability of making a Type I Error? (1)

What is the difference between a Type I and Type II Error? (2)

n (number of people in your sample): (1)

(standard error of the mean): (2)

0.78/square root 30= 0.14

Computed Z score: (3)

p value (round to 3 decimal places) (1):

Interpret your result. (5)

Indicate the raw score(s) for a 95% confidence interval around your sample’s M. (2)

2.8-2(0.78) and 2.8+2(0.78) = (1.24, 4.36)

Indicate the raw score(s) for a 99% confidence interval around your sample’s M. (2)

2.8-3(0.78) and 2.8+3(0.78) = (0.46, 5.14)

Compute your Effect Size (using Cohen’s d): (3)

What is the magnitude of your effect size (i.e., large, medium, small, etc.) (1)

Answer 1

Answer:----

Probability of making a Type I Error is

Type 1 error is alpha = 0.05. That is 5% or a probability of 5 in 100

The difference between a Type I and Type II Error

1. Type 1 errors also called as FALSE POSITIVES are defined as "rejecting a true null

2. hypotheses by calling it false"

3. Type 2 errors also called as FALSE NEGATIVES are defined as "accepting a false

4. null hypotheses by saying it is true".

5. Therefore, a Type 1 error is more serious than a Type 2 error. But in common language,

6. So, the Type 1 errors occur when we reject something (a genuine product, a suitable candidate, a great date) that should have been accepted.

7. While a Type 2 error is accepting something that should have been rejected (a defective product, a fake candidate, a bad date).

Note that in statistics by definition, a 'null' hypotheses always is phrased as 'there is no difference', 'there is no relation', 'there is no impact' and so on.

Standard error of the mean:

Given,

σ =.0.76

square root 30

the mean =

               =0.76/ = 0.1387

Computed Z score :

z = (2.8 -5)/0.1387 = -15.86.

A z score of over -3 indicates that the sample is highly unusual.

p value (round to 3 decimal places ):

the p-value cannot be calculated for the computed z score.

the raw score(s) for a 95% confidence interval around your sample’s M & the raw score(s) for a 99% confidence interval around your sample’s M

The raw score is given by the formula: raw score = mean + (z score)(standard deviation)

At 95% confidence interval, the raw score = 2.8 =/- 1.96(0.78)

Lower boundary = 1.2712 & Upper boundary = 4.3288

At 99% confidence interval, the raw score = 2.8 =/- 2.58(0.78)

Lower boundary = 0.7876 & Upper boundary = 4.8124

.Effect Size (using Cohen’s d):

M1:5

M2:2.8

SD₁:0.76

SD₂:0.78

Then,

Cohen's d =M1-M2/root(((SD₁)²+( SD₂)²/2)

                 =   (5-2.8)/root(((0.76)²+(0.78)²/2)

                  = 2.85

The magnitude of your effect size (i.e., large, medium, small, etc.) :

As Cohen's d is >2, we can say that the effect size is 'Huge'.