Question

The test scores dropped in 2009. Design and run a hypothesis test to determine if the decline represented a statistically significant decrease in the mean test score. Be sure to explain how you plan set up the test. You will need to decide what you will use as your population. Be sure to explain the result and implications of the hypothesis test.

Test Data can be found here: https://docs.google.com/spreadsheets/d/e/2PACX-1vSdSY0cbi4CdW1509-B3HVVGL1t8AieqCPw8nroXMXup8q1Rll3huy8qiCzMphB-DsCOlJ6fNsxlzUO/pubhtml

Answer 1

As per the data we can consder the student marks for all the years can be considered as population data since we have a large number of data.

Student marks of year 2009 can be considered a sample taken from the poupulation data.

To check whether 2009 marks of students declined we can perform one sided one sample t-test using = 5%

Hypothesis:-

( Sample mean = Population mean)

( Sample mean is less than Population mean)

From the data we can find the following parameters

Population mean µ	59.66
Std. deviation of population ?	5.28
Sample mean	58.47
Sample Std. Deviation (S)	5.59
No of observations in sample	210

test statistic

since this is a left tail test criteria for rejection oh null hypothesis is

here it clearly seen that -3.084 is less than -1.645 i.e., we reject null Hypothesis.

Students marks for year 2009 are significantly different. That is marks are declined in this year.