# Are population means score in statistics different between 2006 and 2016 students? ( Help ) (Stats)

##### 1 Answer

Part a) No, there is not a significant difference between 2006 and 2016 students' test scores.

Part b) Interval:

#### Explanation:

*Part A*

We want to determine whether there is a significant difference between the population mean scores of the students. We will test the hypotheses:

where "y" represents data from 2016, and "x" represents data from 2006.

We can conduct a **two-sample t-test** for the difference between two means using a significance level

- Random: both samples (2006 and 2016) are random samples
- 10% condition / Independence: We must assume that the population of test takers ...
- in 2006 is greater than 140
#N_x >= 10*14# - in 2016 is greater than 200
#N_y >= 10*20# - Large/Normal samples: We must assume that the distributions for both populations are each approximately Normal

The formula for the test statistic t is:

with degrees of freedom (using the lower n)

Substitute values:

Now, using the table of t critical values or a calculator, we can find that our

(Using a calculator):

Since our **There is not convincing evidence of a significant difference** between 2006 and 2016 tests.

*Part B*

We want to construct a 95% confidence interval for the difference between two means.

We can use a **two-sample t-interval** . The conditions for inference were verified in part (a).

The formula for the two-sample t-interval with 95% confidence is:

Substitute values:

Find t* using the table of critical t* values (linked above). This is where we specify the 95% confidence.

We are 95% confident that the interval from