Lab Activity 4 Math 113 Name : _________________ 10 Pts Intro to Applied Stats

## All hypothesis testing is done under the assumption the null hypothesis is true.

If we obtain results that are too unusual to occur just by chance if the null hypothesis is true, then our assumption must be wrong and we reject our null hypothesis.

The mass of several Tootsie-Roll Pop's was collected earlier in the year. The summary information is given in the table below.
 Flavor n Mean Std Dev Cherry 28 17.1668 0.5013 Chocolate 12 17.1633 0.8804 Grape 8 17.2450 0.5331 Orange 2 17.1750 0.0636 Raspberry 13 16.7585 0.6079 Total 63 17.0921 0.6170

We will be examining the mean of samples.

1. The sample size was ________.
2. The Central Limit Theorem says that the sample mean will have a normal population if the sample came from a normal population or an approximately normal distribution if the sample size is sufficiently large.
1. How large is sufficiently large?
2. Can we say that the sample mean is at least approximately normally distributed?
3. Consider the standard deviations given in the table.
1. Are they the population standard deviations or the sample standard deviations?
2. Based on your answer to 3.a, should we be using the Normal distribution or the Student's t distribution?

4. Test the claim that a Tootsie Roll Pop has a net mass of 17.0 g. Even though the claim is about a single Tootsie Roll Pop, we will test the mean of several Pops.
1. The claim, written symbolically is ______________.
2. The original claim is the ___________ hypothesis.
3. The Null Hypothesis is: H0: ___________.
4. The Alternative Hypothesis is: H1: ___________.
5. This is a (left tail, right tail, two-tail) test.
6. The level of significance isn't given, so use alpha = ___________.
7. The sample size is ___________.
8. There are ___________ degrees of freedom.
9. The critical value(s) is/are ___________.
10. The formula for the test statistic is:

11. Compute the test statistic.

12. Draw a figure with the critical region(s) shaded and the critical value(s) and test statistic labeled

13. The test statistic (does / does not) lie in the critical region.
14. The decision is to (reject / fail to reject) the null hypothesis.
15. There is (sufficient / insufficient) evidence at the ___________ level of significance to (reject / support) the claim that the net mass of a Tootsie Roll-Pop is 17.0 g.
16. Probability-Value approach
1. Find the probability of being more extreme than your test statistic. More extreme is defined in terms of type of test. If it's a right tail test, find the probability of being greater than the test statistic. If it's a left tail test, find the probability of being less than the test statistic. If it's a two-tail test, find the probability of being greater than the test statistic (if the test statistic is positive) or less than the test statistic (if the test statistic is negative) and then double the value for the other side.

2. Is your probability-value less than the level of significance?
3. Are the results we got unusual at our level of significance?

5. A Normal Probability Plot (also called a Q-Q Plot) is another way of measuring Normality. A Quantile-Quantile Plot is a way to compare the quantiles (generic term for deciles, quartiles, percentiles, etc) of your sample against the quantiles of a known population. If the plot is linear, then the sample comes from that population. A Normal Probability Plot is a Q-Q Plot with the known population being Normal. From the Normal Probability Plot, does the data appear to come from a normal population (yes/no)?

6. You may be wondering why the Q-Q Plot was necessary when we have such a large sample. If we consider any one of the individual flavors, then the sample size is not sufficiently large. What is one requirement of using the Student's t distribution that suggests a Normal Probability Plot should be done (pg 307, 378)?

7. At a 0.10 level of significance, test the claim that we're being cheated on the mass Raspberry Tootsie Roll Pops.
1. The claim, written symbolically is ______________.
2. The original claim is the ___________ hypothesis.
3. The Null Hypothesis is: H0: ___________.
4. The Alternative Hypothesis is: H1: ___________.
5. This is a (left tail, right tail, two-tail) test.
6. The level of significance is alpha = ___________.
7. The sample size is ___________.
8. There are ___________ degrees of freedom.
9. The critical value(s) is/are ___________.
10. The formula for the test statistic is:

11. Compute the test statistic.

12. Draw a figure with the critical region(s) shaded and the critical value(s) and test statistic labeled

13. The test statistic (does / does not) lie in the critical region.
14. The decision is to (reject / fail to reject) the null hypothesis.
15. There is (sufficient / insufficient) evidence at the ___________ level of significance to (reject / support) the claim that (re-write the claim)

8. Test the claim that Cherry flavored Pops have a higher mass than Raspberry flavored Pops.
1. The samples are (independent/dependent).
2. The claim, written symbolically is ______________.
3. The original claim is the ___________ hypothesis.
4. The Null Hypothesis is: H0: ___________.
5. The Alternative Hypothesis is: H1: ___________.
6. This is a (left tail, right tail, two-tail) test.
7. The level of significance is alpha = ___________.
8. The sample sizes are ___________ and __________..
9. There are ___________ degrees of freedom.
10. The critical value(s) is/are ___________.
11. The formula for the test statistic is:

12. Compute the test statistic.

13. Draw a figure with the critical region(s) shaded and the critical value(s) and test statistic labeled

14. The test statistic (does / does not) lie in the critical region.
15. The decision is to (reject / fail to reject) the null hypothesis.
16. There is (sufficient / insufficient) evidence at the ___________ level of significance to (reject / support) the claim that (re-write the claim)