5. [/5 Points] DETAILS MENDSTATC4 10.E.070. MY NOTES ASK YOUR TEACHER I PRACTICE ANOTHER The SAT subject tests in chemistry and physics for two groups of 11 students each electing to take these tests are given below. Chemistry Physics =643 ;=657 5:113 5:105 n=11 n=11 To use the two-sample t-test with a pooled estimate of 02, you must assume that the two population variances are equal. Test this assumption using the F-test for equality of variances. (Use a = 0.05.) State the null and alternative hypotheses. O H0: 012 # 0'22 versus Ha: 0'1 = (12 O H0: 012 = 022 versus Ha: 01 0'2 0 H0: 612 = 622 versus Ha: 01 > 62 O H0: 012 = 2122 versus Ha: 01 < 52 O H0: 012 < (:22 versus Ha: 51 > a2 State the test statistic. (Round your answer to two decimal places.) F : State the rejection region. (Round your answer to two decimal places.) F > State the conclusion. 0 H0 is rejected. There is insufficient evidence to indicate that the variances are different. 0 H is not rejected. There is insufcient evidence to indicate that the variances are different. 0 O H is not re'ectecl. There is sufficient evidence to indicate that the variances are different. 0 J O H0 is rejected. There is sufficient evidence to indicate that the variances are different. What is the approximate p-value for the test? 6. [-/5 Points] DETAILS MENDSTATC4 10.E.073. MY NOTES ASK YOUR TEACHER Quarterbacks not only need to have a good passing percentage, but they need to be consistent. That is, the variability in the number of passes completed per game should be small. The table below gives the number of passes completed for Ben Roethlisberger and Aaron Rodgers, quarterbacks for the Pittsburgh Steelers and Green Bay Packers, respectively, during the 2010 NFL season. t Aaron Rodgers Ben Roethlisberger 19 21 7 16 20 19 15 25 19 22 34 27 19 17 21 12 22 17 23 27 26 30 22 18 21 18 15 (a) Does the data indicate that there is a difference in the variability in the number of passes completed for the two quarterbacks? Use a = 0.01. State the null and alternative hypotheses. O Ho: 012 = 02 2 versus Ha: 012 < 0 2 O Ho: 0 12 = 02 2 versus Ha : 012 > 02 O Ho: 01 2 # 02 2 versus Ha: 012 = 02 O Ho: 012 <022 versus ha: 012> 02 O Ho: 012 = 022 versus Ha: 012 # 022 State the test statistic. (Round your answer to two decimal places.) F = State the rejection region. (Round your answer to two decimal places.) F > State the conclusion. O Ho is not rejected. There is insufficient evidence to indicate a difference in the variability. O Ho is rejected. There is insufficient evidence to indicate a difference in the variability. O Ho is not rejected. There is sufficient evidence to indicate a difference in the variability.7. [-/7 Points] MENDSTATC4 10.E.075. ASK YOUR TEACHER PRACTICE ANOTHER A pharmaceutical manufacturer purchases a particular material from two different suppliers. The mean level of impurities in the raw material is approximately the same for both suppliers, but the manufacturer is concerned about the variability of the impurities from shipment to shipment. If the level of impurities tends to vary excessively for one source of supply, it could affect the quality of the pharmaceutical product. To compare the variation in percentage impurities for the two suppliers, the manufacturer selects 8 shipments from each of the two suppliers and measures the percentage of impurities in the raw material for each shipment. The sample means and variances are shown in the table. Supplier A Supplier B )7, = 1.88 E2 = 1.83 2 _ 2 _ s1 0.272 s2 0.093 n1 = 8 n2 = 8 (a) Do the data provide sufcient evidence to indicate a difference in the variability of the shipment impurity levels for the two suppliers? Test using a = 0.01. Based on the results of your test, what recommendation would you make to the pharmaceutical manufacturer? (Round your answers to two decimal places.) 1-2. Null and alternative hypotheses: O H0: 012 022 versus Ha: 012 = 522 O H0: 012 = 0'22 versus Ha: 0'12 $ 022 O H0: (712 = (722 versus Ha: 712 > 0'22 0 H0: 012 = 0'22 versus He: 612 < 0'22 . 2 2 . 2 2 OHO.a1 <02 versusha.r1>02 3. Test statistic: F = C] 4. Rejection region: F > 8. [-l15 Points] MENDSTATC414.E.008.MI.SA. ASK YOUR TEACHER PRACTICE ANOTHER This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise A peony plant with red petals was crossed with another plant having streaky petals. A geneticist states that 75% of the offspring from this cross will have red flowers. To test this claim, 100 seeds from this cross were collected and germinated, and 55 plants had red petals. Use the chi-square goodness-of-fit test to determine whether the sample data confirm the geneticist's prediction. (Use it = 0.01. Use p1 for the probability of having red flowers and p2 for the probability of having Streaky petals.) State the null and alternative hypotheses. Find the test statistic. Find the rejection region. State your conclusion. MENDSTATC4 14.E.018. | MY NOTES | ASK YOUR TEACHER I PRACTICE ANOTHER A survey of 400 respondents produced these cell counts in a 2 x 3 contingency table. 11. [-/6 Points] Columns Rows 1 2 3 Total 1 38 34 92 164 2 67 58 111 236 Total 105 92 203 400 (a) If you wish to test the null hypothesis of "independence\"that the probability that a response falls in any one row is independent of the column it falls inand you plan to use a chi-square test, how many degrees of freedom will be associated with the 12 statistic? degrees of freedom (b) Find the value of the test statistic. (Round your answer to three decimal places.) X2 = (c) Find the rejection region for a = 0.01. (Round your answer to three decimal places.) X2> MENDSTATC4 14.E.021 . ASK YOUR TEACHER PRACTICE ANOTHER A study was conducted to determine the effect of early child care on infant-mother attachment patterns. In the study, 96 infants were classied as either \"secure\" or "anxious" using the Ainsworth strange situation paradigm. In addition, the infants were classified according to the average number of hours per week that they spent in child care. The data are presented in the table. 12. [-/5 Points] Low Moderate High (0-3 hours) (4-19 hours) (20-54 hours) Secure 23 37 7 Anxious 9 11 9 (a) Do the data provide sufficient evidence to indicate that there is a difference in attachment pattern for the infants depending on the amount of time spent in child care? Test using a = 0.05. State the null and alternative hypotheses. O Ho: Attachment pattern and amount of time spent in child care are linearly related. Ha: Attachment pattern and amount of time spent in child care are independent. 0 Ho: The number of secure and anxious children are equal. Ha: The number of secure and anxious children are not equal. 0 Ho: Attachment pattern and amount of time spent in child care are independent. Ha: Attachment pattern and amount of time spent in child care are linearly related. 0 Ho: Attachment pattern and amount of time spent in child care are dependent. Ha: Attachment pattern and amount of time spent in child care are independent. 0 Ho: Attachment pattern and amount of time spent in child care are independent. Ha: Attachment pattern and amount of time spent in child care are dependent. Find t1e test statistic. (Round your answer to three decimal places.) X2 = Find the rejection region. (Round your answer to three decimal places.) X2>