well-known ice cream store tested two different methods for scooping ice cream s
ID: 3179633 • Letter: W
Question
well-known ice cream store tested two different methods for scooping ice cream so they can use the method that has the least weight variability in their training of new and current employees. Ice cream cones scooped sample weights follow.
Research Question: At level of significance = 0.05, do the two methods have equal variability?
Method 1
Method 2
4.7
3.6
3.7
4.1
3.2
3.9
3.8
5.5
3.9
4.1
4.8
4.7
3.5
4.9
5.1
3.5
4.8
3.9
5.3
3.8
3.3
4.8
4.2
5.0
5.3
4.4
4.6
1. Mark or highlight the correct hypotheses (Choose carefully as several answers depend on HA)
H0: 12 22, HA: 12 < 22
H0: 12 22, HA: 12 > 22
H0: 12 = 22, HA: 12 22
2. The selected Hypotheses in question 1
Have a two-tailed test with lower and upper reject regions
Have a one-tailed test with lower reject region
Have a one-tailed test with upper reject region
3. Alpha is the probability of a type 1 error, the risk we are willing to take of rejecting H0 when it's true.
The critical value(s) bound the reject region(s) with probability alpha.
Pvalue is the probability of an equal or more extreme test statistic computed assuming H0 is true.
Mark the two Decision Rules for rejecting H0 that apply to this problem.
Test statistic > positive critical value of upper tail test
Test statistic < negative critical value of lower tail test
Test statistic falls outside interval (negative critical value of lower tail, positive critical value of upper tail) of two-tailed test.
pvalue <
4)
What are the following values as displayed below for the HA matching this problem?
Test statistic =
Reject Region =
Critical Value(s) =
pvalue =
6. The rules selected in question 3 indicate that
The evidence against H0 is significant. H0 is rejected
The evidence against H0 is not significant. H0 is not rejected
7. In every day non-statistical language,
You conclude the two scooping methods have equal variability.
You conclude the two scooping methods have unequal variability.
Method 1
Method 2
4.7
3.6
3.7
4.1
3.2
3.9
3.8
5.5
3.9
4.1
4.8
4.7
3.5
4.9
5.1
3.5
4.8
3.9
5.3
3.8
3.3
4.8
4.2
5.0
5.3
4.4
4.6
Explanation / Answer
1) H0: 12 = 22, HA: 12 22
2) Have a two-tailed test with lower and upper reject regions
3)3. Alpha is the probability of a type 1 error, the risk we are willing to take of rejecting H0 when it's true. alpha =0.05
critical values F>2.9633 and 0.3147>F
The critical value(s) bound the reject region(s) with probability alpha.
3)rejection:
Test statistic falls outside interval (negative critical value of lower tail, positive critical value of upper tail) of two-tailed test.
pvalue <
4) test stat : F =1.3621
rejection region p <0.025 or p>0.975
critical region:F>2.9633 and 0.3147>F
pvalue =0.5644
6) The evidence against H0 is not significant. H0 is not rejected
7) You conclude the two scooping methods have equal variability.
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