File - Ms. Struthers` Classroom

AP Statistics
Name: _____________________
Lesson 9-2 Conducting Significance Tests
Recap:
Tests of Significance
Stating a Hypothesis
Null Hypothesis:
Alternative Hypothesis:
Ex. #1 In the past, the mean score of the seniors at XYZ Secondary on the Euclid contest has been 50. This
year a special preparation course is offered and all 53 seniors planning to take the contest enrol in the
course. The mean of their 53 contest scores is 54.1. The principal believes that the new course has
improved the students’ contest scores. Assume that the contest scores for seniors at XYZ secondary
vary normally with a standard deviation of 8.
a)
Identify the population and parameter of interest.
b)
State the hypothesis that you would use to test the principals’ claim. Use both words and
symbols.
Test Statistic and Conditions:
-
A test statistic is used for calculating the x-score for the sample mean
Conditions for using a significance test:
SRS, normality, and independence
These three conditions must be verified before performing a significance test about a population
mean/proportion
-
If these three conditions are met then the distribution of x is normal with a standard deviation of
Test statistic =
estimate( x) − hypothesised value
σ
n
σ
n
AP Statistics
This is a z-score!
Name: _____________________
** note for today’s class we are assuming we know the standard deviation of the
population, that is not always the case!
P-value
Probability against the null hypothesis, if it was true.
Small p-value, the null hypothesis (Ho) is unlikely, the results from the sample did not occur by chance
or sampling variability, change did occur
2-Tailed test P-value = P ( z < −α ) + P ( z > α )
1-Tailed test Ha: µ < k
P-value P ( z < −α )
P-value P ( z > α )
Ha: µ > k
Ex. #1 A hospital monitors paramedic response times. Last year the average response time was 6.7 minutes
( σ = 2 min ). This year a sample of 400 responses had an average of 6.48 minutes. The hospital wants
evidence that response time have decreased?
a) State the null and alternative hypothesis
b) Calculate the test statistic and the p-value. Is there evidence that the response time has decreased at
a 5% level of significance?
AP Statistics
Name: _____________________
Ex. #2 In the past, the mean score of the seniors at XYZ Secondary on the Euclid contest has been 50. This
year a special preparation course is offered and all 53 seniors planning to take the contest enrol in the
course. The mean of their 53 contest scores is 54.1. The principal believes that the new course has
improved the students’ contest scores. Assume that the contest scores for seniors at XYZ secondary
vary normally with a standard deviation of 8. (Lesson 11.2 – note change to value of standard
deviation)
Use our Four Steps Process to find evidence that the contest scores have/have not increased.
AP Statistics
Ex. #3
Name: _____________________
Bottles of cola are supposed to contain 300 ml of cola. There is some variation from bottle to
bottle. The distribution of the volume of cola is normal with a standard deviation of 3 ml. An
inspector suspects that the bottles are under filled and randomly selects six bottles form the same
day to check. Given the results of his check, is there convincing evidence that the mean amount
of cola in all the bottles filled that day is less than 300 ml? Use a significance level of α = 0.05 .
Results: 295.4, 296.7, 300.9, 297.9, 299.2, 297.0
Homework:
b)
Would your conclusion be any different if the significance level was α = 0.01?
c)
If you were the cola manufacturer, which significance level would you be likely to use?
pg. 546 #1-25 odd and 27-30 (M/C)