Chapter 8
The video above is from a past semester. The material is the same but any dates mentioned will be incorrect. For the current term, please refer to the due dates in syllabus.
This first section is several different pieces that will all be put together in the next section. So in section 8.1 our goal is to learn how do do these individual pieces. We'll make sense of them in the next section.
(#6 and #7) Identifying Ho and H1.
Express the original claim in symbolic form.
Identify the null and alternative hypotheses.
8-1 #6 Claim: Fewer than 95% of adults have a cell phone. In a Marist poll of 1128 adults, 87% said that they have a cell phone.
Use the below table to help with the final conclusion wording. This can be tricky without following the chart.
Section 8-2 Testing a Claim about a Proportion
Assumptions:
Sample is a SRS (simple random sample)
Binomial distribution conditions are satisfied
a) fixed number of trials
b) independent
c) success/failure (2 outcomes)
d) constant probabilities
3) np>5 and nq>5 (there are at least 5 successes and 5 failures)
Critical value method:
If the test stat is more extreme than the critical value, reject Ho. Otherwise, fail to reject Ho.
P-value method:
If the p-value < alpha(significance level) , reject Ho. Otherwise, fail to reject Ho.
Final conclusions can be tricky!! I highly recommend using page 366 (table 8-3 , picture above) for direction on wording.
Please see the statcrunch directions for the above hypothesis tests (Very helpful). These directions can be found here...Statcrunch directions
Note for below problem: A couple of friends and I do quite a bit of fishing off the coast of Northern California in the summertime. We catch a variety of different fish and some have the characteristics that can be concerning for having high levels of mercury (predatory fish or slow growing). The only data we could find for our area was severely lacking, so we decided to collect and analyze the data ourselves through a grant from Humboldt Bay Keeper. Below is a subset of our data from our catch of Lingcod ( a large predatory fish that lives on the bottom, the picture is of my son with a Lingcod). Were our concerns of high mercury legit?
Please see the statcrunch directions for the below hypothesis tests (Very helpful). These directions can be found here...Statcrunch directions
For the below problem, we need to use statcrunch...stat, proportion stats, one sample, with DATA.
The Office of Environmental Health Hazard Assessments (OEHHA) "do not consume" level of Methyl-Mercury is 0.44 ppm for women under 45 and children. Use a 0.05 significance level to test claim that Methyl-Mercury in Lingcod is greater than 0.44 ppm. What does this suggest about women under 45 and children eating Lingcod?
Methyl- Mercury (ppm) for Lingcod:
0.137 0.452 0.341 0.226 0.238 0.484 0.408 1.94 0.789 0.55 0.72 1.49 1.59 2.84 0.193 0.171 0.537 0.655 Note: The sample size is n=18 and data is only somewhat normally distributed. It would be better if we had a few more in the sample to better meet the requirement for this T test.
Solution: Here raw data is given so the use of Statcrunch is a huge time and calculation saver. Enter the data into a column of Statcrunch, click Stat, T-Stat, One-sample, with data. Select the data set and enter in Ho (=0.44) and Ha (>0.44) for the hypothesis test You should get the following:
One sample T hypothesis test:
μ : Mean of variable
H0 : μ = 0.44
HA : μ > 0.44
Hypothesis test results:
Variable Sample Mean Std. Err. DF T-Stat P-value
Methyl-Mercury 0.7645 0.17275369 17 1.8783969 0.0388
Since the p-value (0.0388) is less that the significance value (0.05), we reject Ho. There is sufficient evidence to support the claim that Methyl-Mercury in Lingcod is greater than 0.44 ppm. Simply put, Lingcod have high levels of Methyl-Mercury and women under 45 and children should avoid eating them.