case study 4
Chapter 10 One Sample Hypothesis Testing
A hypothesis test is used when a researcher wants to test a previous statistic to see if it is different now than it was before. In order for s statics to change the new survey must provide significant evidence that the statistic has changed.
Hypotheses:
1. Null hypothesis, is the original statement or statistic that has been verified. Always in the form of
2. Alternate hypothesis, The statement or claim that is being tested.
Choices:
1. Reject
2. Fail to reject
We make our choice based on the P-value. A P-value is the probability that a random sample would give the results in this second survey. The further the survey results are from the original the smaller the probability, because these significant changes are not just by chance.
Proportions
Information you will be given:
· Percentage/proportion from a prior study
· New survey total polled
· New survey amount that answered a certain way
· Level of significance
· Statement about a new claim
In 1997, 46% of Americans said they did not trust the media “when it comes to reporting the news fully, accurately and fairly”. In a 2007 poll of 1010 adults nationwide, 525 stated they did not trust the media. At the α = 0.05 level of significance, is there evidence to support the claim that the percentage of Americans that do not trust the media to report fully and accurately has increased since 1997?
By Statcrunch: Stat->Proportion Stats->One sample->with summary
Those in favor->
Total surveyed->
Select Hypothesis test->
Enter null and alternate based -> on the previous studies and new claim
Compare P to
· If Reject
· If Fail to Reject
Writing a conclusion
1. If you reject: There is sufficient evidence that the proportion of the population that _____ is __ ”claim”___
2. If you do not reject: There is NOT sufficient evidence that the proportion of the population that _____ is __ ”claim”___
Means
Information you will be given:
· Mean from a previous study
· Number of people surveyed
· New study mean
· New study standard deviation
· Level of significance
· Statement about a new claim
According to the American Time Use Survey, the typical American spends 154.8 minutes per day watching television. Do Internet users spend less time each day watching television? A survey of 50 Internet users results in a mean time watching television per day of 128.7 minutes, with a standard deviation of 46.5 minutes. Conduct the appropriate test to determine if Internet users spend less time watching television at the level of significance.
By Statcrunch: Stat->T-stats->One sample->with summary
Sample Mean->
Sample Standard deviation ->
Sample size->
Select Hypothesis test->
Enter null and alternate based -> on the previous studies and new claim
Compare P to
· If Reject
· If Fail to Reject
T-Statistic similar to Z-score
Writing a conclusion
1. If you reject: There is sufficient evidence that the mean of the population that _____ is __ ”claim”___
2. If you do not reject: There is NOT sufficient evidence that the mean of the population that _____ is __ ”claim”___
Standard Deviation/Variance
Information you will be given:
· Standard Deviation from the population
· Number of items surveyed
· New study standard deviation
· Level of significance
· Statement about a new claim
From previous information we know the standard deviation for the resting heart rates of Elgin Community College students was 12bpm. One professor decided to test this claim and got the following heart rates for his students.
Based on this sample, is there enough evidence to say that the standard deviation of the rest heart rates for students in this class is different from 12bpm?
By Statcrunch: enter the data into a column then click Stat->Variance stats->One sample->with data
Select the column ->
Select Hypothesis test ->
Enter the VARIANCE ->
Variance = standard deviation squared
Test Stat P-Value
Compare P to
· If Reject
· If Fail to Reject
Writing a conclusion
1. If you reject: There is sufficient evidence that the standard deviation of the population that _____ is __ ”claim”___
2. If you do not reject: There is NOT sufficient evidence that the standard deviation of the population that _____ is __ ”claim”___