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In: Statistics and Probability

Question 6: An English professor believes that the average grade on an English essay in a...

Question 6: An English professor believes that the average grade on an English essay in a particular school system for females is higher than for males. A random sample of 31 females had a mean score of 82 with a standard deviation of three, and a random sample of 25 males had a mean score of 76 with a standard deviation of four. Does the data agree with this professor?

a) Is this an observational study or an experiment?

b) Identify (and classify) the explanatory and response variables.

c) Summarize the information in this question into a table.

d) Create a 95 % confidence by using the statistical process. You do not have to visualize the assumptions or the data for this question.

Solutions

Expert Solution

a) Is this an observational study or an experiment?

Ans - It is an experiment as the data is collected and studied the claim.

b) Identify (and classify) the explanatory and response variables.

Ans - Response variable - average grade on an English essay in a particular school system for FEMALES

Independent Variable - average grade on an English essay in a particular school system for MALES

c) Summarize the information in this question into a table.

Ans -

Female Male
Average 82 76
SD 3 4
Sample Size 31 25

d) Create a 95 % confidence by using the statistical process. You do not have to visualize the assumptions or the data for this question.

Ans - Here we will compute the confidence interval for mean for FEMALES,

The computation is as follows

Sample size n = 31
Sample mean X̄ = 82
Sample standard deviation σ = 3
Z-score for 95% confidence level = 1.960

= 82 ± 1.96035.5678
= 82 ± 1.960 x 0.5388
= 82 ± 1.056
82 + 1.056 = 83.0561 or 82 - 1.056 = 80.9439

The lower limit is 80.9439 and
The upper limit is 83.0561

orchestra answered 2 years ago
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