Q #1

7. [0.58/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 8.5.011. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A random sample of n, = 49 measurements from a population with population standard deviation , = 5 had a sample mean of x, = 8. An independent random sample of 72 = 64 measurements from a second population with population standard deviation , = 6 had a sample mean of x2 = 11. Test the claim that the population means are different. Use level of significance 0.01. (a) Check Requirements: What distribution does the sample test statistic follow? Explain. O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's t. We assur e approximately normal with known standard deviations. The standard normal. We assume th ons are approximately normal with known standard deviations. O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. (b) State the hypotheses. O Ho: My = #2: H1 : H1 & H2 (c) Compute *1 - *2. * 1 - *2 = Compute the corresponding sample distribution value. (Test the difference (, - /2. Round your answer to two decimal places.) (d) Find the P-value of the sample test statistic. (Round your answer to four decimal places.)8. [0.48/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 8.5.013.MI.S. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER For one binomial experiment, n. = 75 binomial trials produced r, = 30 successes. For a second independent binomial experiment, no = 100 binomial trials produced ry = 50 successes. At the 5% level of significance, test the claim that the probabilities of success for the two binomial experiments differ. LA USE SALT (a) Compute the pooled probability of success for the two experiments. (Round your answer to three decimal places.) (b) Check Requirements: What distribution does the sample test statistic follow? Explain. O The standard normal. We assume the population distributions are approximately normal. O The Student's t. We assume the population distributions are approximately normal. O The Student's t. The number of trials is sufficiently large The standard normal. The number of trials is sufficiently large. State the hypotheses. O Ho: P1 = P2' H1 P1 = P2 O HOP1 = P2' Hi! P1 > P2 O HOP1 M2 O HO: H1 # #23 H1 H1 = H2 (b) What sampling distribution will you use? What assumptions are you making? O The Student's t. We assume that both population distributions are approximately normal with known standard deviations. The standard normal. We assume that both population distributions are approximately normal with known standard deviations. O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. What is the value of the sample test statistic? (Test the difference /j - /2. Round your answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.)11. [0.36/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 8.5.019.MI.S. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A random sample of n, = 10 regions in New England gave the following violent crime rates (per million population). : New England Crime Rate 3.5 3.7 4.0 4.1 3.3 4.1 1.8 4.8 2.9 3.1 Another random sample of no = 12 regions in the Rocky Mountain states gave the following violent crime rates (per million population). x2: Rocky Mountain Crime Rate 3.7 4.1 4.7 5.5 3.3 4.8 3.5 2.4 3.1 3.5 5.2 2.8 LO USE SALT Assume that the crime rate distribution is approximately normal in both regions. (a) Use a calculator to calculate x1. $1. X2 and $2. (Round your answers to four decimal places.) * 1 Do the data indicate that the violent crime rate in the Rocky Mountain region is higher than in New England? Use a = 0.01. (i) What is the level of significance? State the null and alternate hypotheses. O Ho: My = My Hilly > H2 (ii) What sampling distribution will you use? What assumptions are you making? O The standard normal. We assume that both population distributions are approximately normal with known standard deviations. O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's t. We assume that both population distributions are approximately normal with known standard deviations. The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. What is the value of the sample test statistic? (Test the difference /, - #2. Round your answer to three decimal places.)12. [0.5/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 8.5.027. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Given x, and X2 distributions that are normal or approximately normal with unknown @, and 62. the value of t corresponding to x1 - x2 has a distribution that is approximated by a Student's t distribution. We use the convention that the degrees of freedom is approximately the smaller of n, - 1 and n2 - 1. However, a more accurate estimate for the appropriate degrees of freedom is given by Satterthwaite's formula: d.f. (1) 712 - 1 (7 where s1. 52. nyr and ny are the respective sample standard deviations and sample sizes of independent random samples from the x, and x2 distributions. This is the approximation used by most statistical software. When both n, and my are 5 or larger, it is quite accurate. The degrees of freedom computed from this formula are either truncated or not rounded (a) We tested whether the population average crime rate /2 in the Rocky Mountain region is higher than that in New England, (, . The data were n, = 15, x, 2 3.51, s, 2 0.91, n2 = 12, x2 2 3.87, and s2 2 0.97. Use Satterthwaite's formula to compute the degrees of freedom for the Student's t distribution. (Round your answer to two decimal places.) d.f.13. [0.75/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 8.5.028.5. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider independent random samples from two populations that are normal or approximately normal, or the case in which both sample sizes are at least 30. Then, if , and 62 are unknown but we have reason to believe that , = 62, we can pool the standard deviations. Using sample sizes n, and 2, the sample test statistic x - X2 has a Student's t distribution where * 1 - * 2 t = with degrees of freedom d.f. = n, + n2 - 2 and where the pooled standard deviation s is (71 - 1)s1- + (n2 - 1)=2- 1 + 72 - 2 Note: With statistical software, select the pooled variance or equal variance options. USE SALT (a) There are many situations in which we want to compare means from populations having standard deviations that are equal. This method applies even if the standard deviations are known to be only approximately equal. Consider a report regarding average incidence of fox rabies in two regions. For region I, 7, = 16, x1 2 4.75, and s, = 2.82 and for region II, n2 = 15, x2 P2 Ho: P1 = P2 Hil P1 = P2 O Ho: P1 = P2' Hip1 * P2 (b) What sampling distribution will you use? What assumptions are you making? The standard normal. The number of trials is sufficiently large. The Student's t. The number of trials is sufficiently large. O The Student's t. We assume the population distributions are approximately normal. O The standard normal. We assume the population distributions are approximately normal. What is the value of the sample test statistic? (Test the difference p, - P2. Do not use rounded values. Round your final answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.)15. [0.4/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 8.5.036. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adultst. Assume that REM sleep time is normally distributed for both children and adults. A random sample of n, = 11 children (9 years old) showed that they had an average REM sleep time of x, = 2.9 hours per night. From previous studies, it is known that , = 0.6 hour. Another random sample of 72 = 11 adults showed that they had an average REM sleep time of x2 = 2.40 hours per night. Previous studies show that 2 = 0.8 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 5% level of significance. Solve the problem using both the traditional method and the P-value method. (Test the difference /j - (2. Round the test statistic and critical value to two decimal places. Round the P-value to four decimal places.) test statistic critical value P-value