1. Toyota engineers would like to know the standard deviation in gas mileage of the 2012 Toyota Sienna. They calculated the gas mileage of 24 randomly selected 2012 Siennas
24 28 27 24 28 20
23 26 26 25 26 19
23 25 20 28 25 21
24 25 24 25 24 20
(a) Determine the sample standard deviation.
(b) Determine a 97% confidence interval for the standard deviation of all 2012 Toyota Siennas.
(c) State your final confidence interval result in a sentence that interprets the result within the context of the situation.
5. Listed on the right are the measured radiation emissions (in W/kg) corresponding to a sample of different types of cell phones. Use a 0.1 significance level to test the claim that cell phones have a mean radiation level that is less than 1.00 W/kg. Different cell phones radiation emissions
0.38 0.55 1.54 1.55
0.92 0.96 1.00 0.86
(a) Give the null and alternative hypotheses for this situation in mathematical notation.
(b) Based upon a 10% level of significance, determine the critical value(s) associated with this hypothesis test.
(c) Determine the sample’s test statistic.
(d) Do you reject or fail to reject the null hypothesis?
(e) State a final conclusion regarding the results of the hypothesis test. Make sure your statement is specific to context of this problem and involves supporting or rejecting the claim (or not supporting / not rejecting it).
6. In a poll, 790 adults were asked to identify their favorite seat when they fly on a plane, and 431 of them chose a window seat. Use a 0.01 significance level to test the claim that the proportion of adults who prefer window seats is greater than 50%.
(a) List the null and alternative hypotheses for this test.
(b) Determine the value of the sample’s test statistic.
(c) Determine the P-value.
(d) Do you reject or fail to reject the null hypothesis?
(e) Write a final interpretive sentence (like in part (e) of problem #5).
7. Self-reported heights and measured heights of twelve males aged 13 – 18 are shown in the table to the right. At the 5% significance level, is there sufficient evidence to support the claim that there is no difference between the average reported heights and the measured heights of males aged 13 -18? All measurements are in inches. Note: Hypothesis testing method work must be shown for credit on this problem. Reported Height Measured Height
67 67.9
72 70.5
62 63.1
69 68.3
72 71.9
63 63.2
67 64.5
65 62.4
56 55.6
63 64.2
75 69.1
70 68.1
8. At the right, give an example of a paired data set (with at least 5 pairs) that demonstrates a strong (but not perfect) positive linear correlation. x y
Use the following situation to answer questions 10 to 16: x = Weight y = Price
The table lists weights (in carats) and prices (in dollars) of six diamonds (all of which have the same cut, color, and clarity). Is there a linear correlation between weight and price? 0.3 510
0.4 1151
0.5 1343
0.5 1410
1.0 5669
0.7 2277
10. Produce a scatterplot of this paired data at the right.
12. Determine the sample’s correlation coefficient r and the coefficient of determination r2. Then explain statistically whether or not the correlation in these two variables is significant.
16. “All mathematical models are wrong, but some are useful.” This quote cautions against overgeneralizing results. For what numeric interval of weights is our trend line equation useful? Would our trend line equation be useful for diamonds with a different cut, color, or clarity than those in the sample? Explain