I've made an attempt to solve these using my TI-84 plus, however I don't know if my approach is correct. Any help is appreciated.
1.) As the costs of prescription drugs escalate, many senior citizens are ordering from or going to Canada to get their medicine. Is there a good reason to go to Canada to buy these drugs? Here are mean prices from stores in the USA & Canada:
USA: $ 290 412 117 139 571 276 484 161 235
Canada: : $ 179 211 72 125 396 171 196 67 156
I think that the two lists are dependent. I put USA in L1 and Canada into L2. Then L2-L1 -> L3
I then ran a T-Test. I think I'm supposed to compared alpha (0.05) to the p-value?
2.) A report by the NCAA states that 57.6 % of football injuries occur during practices. One head trainer claims this number is too high for his conference. In his study, he randomly selects 63 injury cases, fining that 30 occurred during practices. Is his claim correct at a 0.05 level of significance?
I think I have to do a 1-Prop Z Test for this.
I established that H0: p1 = .576 and H1: p1 < .576
I'm not too sure where to go from here.
3.) An anti-smoking group tests 13 random brands of cigarettes to see if there is a relationship between measures of CO (x) and tar (y). If the relationship is considered relevant, estimate the tar measure when the CO measure = 12.
x: 15 17 6 1 8 10 17 11 18 16 10 15 7
y: 1.2 1 .8 .1 .8 1 .7 1.4 1 .8 1.2 .5
I put x into L1 and y into L2. Then I ran the LinReg (a+bx) test. To find a, b, and r.
Since r is close to 1, there is a strong correlation, so the relationship is considered relevant?
1.) To determine if there is a good reason to go to Canada to buy prescription drugs, you can perform a hypothesis test comparing the mean prices in the USA and Canada. Here's how you can approach it on your TI-84 Plus:
- Enter the prices from the USA into List1 (L1) and the prices from Canada into List2 (L2) on your calculator.
- To check if the two lists are dependent, subtract L1 from L2 and store the result in another list, say L3. This gives you the difference in prices between the USA and Canada for each drug.
- Now, you can perform a T-test on the difference list (L3).
- Select "STAT" on your calculator.
- Go to "TESTS" and choose "2-SampTTest."
- Make sure the "μ1" and "μ2" values are set to 0.
- Enter L3 for "L1" and select "Calculate."
After performing the T-test, your calculator will provide a p-value. To determine if there is a good reason to go to Canada to buy drugs, compare the p-value to your chosen significance level (α = 0.05). If the p-value is less than 0.05, you can reject the null hypothesis and conclude that there is a significant difference in prices between the USA and Canada, providing a good reason to go to Canada to buy prescription drugs. Otherwise, you would fail to reject the null hypothesis.
2.) To test the head trainer's claim about the percentage of football injuries occurring during practices, you can use a one-proportion Z-test. Here's how:
- Let p1 be the population proportion of football injuries occurring during practices (claimed by the head trainer) and p̂1 be the observed proportion from the study.
- Set up the hypotheses:
- Null hypothesis (H0): p1 = 0.576
- Alternative hypothesis (H1): p1 < 0.576 (one-sided test)
Now, let's perform the one-proportion Z-test on your TI-84 Plus:
- Select "STAT" on your calculator.
- Go to "TESTS" and choose "1-PropZTest."
- Enter the observed proportion of injuries during practice (30 out of 63) for "x" and the total number of cases (63) for "n."
- Enter the hypothesized proportion (0.576) for "p0" and select the direction of the alternative hypothesis.
- Select "Calculate."
After performing the test, your calculator will provide a p-value. Compare this p-value to your chosen significance level (α = 0.05). If the p-value is less than 0.05, you can reject the null hypothesis and conclude that there is enough evidence to support the trainer's claim. Otherwise, you would fail to reject the null hypothesis.
3.) To estimate the tar measure when the CO measure is equal to 12 and determine if there is a relevant relationship between CO and tar, you can use linear regression analysis. Here's how you can do this on your TI-84 Plus:
- Enter the CO measures (independent variable) into List1 (L1) and the tar measures (dependent variable) into List2 (L2) on your calculator.
- Select "STAT" on your calculator.
- Go to "CALC" and choose "LinReg(ax+b)."
- Specify L1 for "Xlist" and L2 for "Ylist."
- Select "Calculate" or "Graph."
After performing the linear regression analysis, your calculator will provide you with the equation of the regression line (a + bx), where a represents the intercept and b represents the slope. Additionally, your calculator will provide the correlation coefficient (r), which measures the strength and direction of the linear relationship.
If the correlation coefficient (r) is close to 1, as you mentioned, it indicates a strong positive linear correlation between CO and tar measures. This means that as the CO measure increases, the tar measure tends to increase as well. Therefore, there is a relevant relationship between CO and tar measures in this case.
To estimate the tar measure when the CO measure is equal to 12, substitute 12 into the equation of the regression line (a + bx), using the obtained values of a and b from the linear regression analysis. The resulting value will give you an estimate of the tar measure corresponding to a CO measure of 12.