7.On average, what value is expected for the t statistic when the null hypothesis is true? а. О с. 1.96 b. 1 d. t> 1.96
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- 6.4.5-T Assume that females have pulse rates that are normally distributed with a mean of u = 74.0 beats per minute and a standard deviation of o = 12.5 beats per minute. Complete parts (a) through (c) below. a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 78 beats per minute. The probability is 0.6255. (Round to four decimal places as needed.) b. If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 78 beats per minute. The probability is (Round to four decimal places as needed.)a. Let Z ~ Normal(0, 1) be a continuous standard normal random variable with mean of 0 and standard deviation of 1. What is the probability that Z comes out to be less than -1.64? Normal(26.2, 5) is a continuous normal random variable 26.2 and standard deviation of o = 5. What is the probability that b. Suppose instead that X ~ with mean of µ = X comes out to be less than 18? c. Working still with X That is, find a value c such that the probability that X is bigger than c is 2.5%. Normal(26.2, 5), find a value c such that P(X > c) = 0.025.A sample of size 8 has a mean of 71 and a standard deviation of 8.5 is to be used to test the null hypothesis that the population mean is 70 versus it is different from 70, assuming the population is distributed N(u, 25) then the p-value of the test is О a.0.425 Ob. None of these O c. 0.384 O d. 0.407 О е. 0.814
- 13. What is the null hypothesis for the following statement? The average teenager drinks at least 10 cans of soda per week. Αμ > 10 Bu = 10 C με 10 Dμ 210 14. The mileage of returned leased vehicles at a local dealership is normally distributed with a mean of 34,600 and a standard deviation of 3200. What percent of the vehicles are returned with fewer than 30,000 miles? F 5% G 7.5% H 84.9% J 92.5% 15. COMMUTERS Which group should be surveyed to determine how people commute to work in order to produce a random sample? A students in your school B people passing through a toll booth on a given day C people in your state whose last name begins with S D people whose annual income is greater than $1,000,0003. A box should contain exactly 64 matches. 100 boxes were checked and gave • the sample mean ī = 65 and sample standard deviation si00 = 25. 10 • the sample mean ī = 66 and sample standard deviation si00 = 25. In each case verify the hypothesis H(m = 64). [Ans. D = (-, –2, 32) U (2.32, o)] (a) 2 ¢ D hence we fail to reject ; (b)4 € D hence we reject the hypothesis]Q2
- Assume the random variable X has and expected value of 30 and a standard deviation of 8 and the random variable Y has an expected value of 50 and a standard deviation of 14.18Determine the form of a particular solution for the differential equation. Do not solve. y" - y = 3e^4t + 5te^4t +(t^2)(e^4t)
- A nutritionist claims that the mean tuna consumption by a person is 3.3 pounds per year. A sample of 60 people shows that the mean tuna consumption by a person is 3.1 pounds per year. Assume the population standard deviation is 1.07 pounds. At a = 0.1, can you reject the claim? (a) Identify the null hypothesis and alternative hypothesis. Ο Α H0: μ 3.1 Ha: u> 3.1 В. Но: и#3.1 Ha: H= 3.1 c. H0 μ>3.1 Ha: us3.1 D. Ho:µ=3.3 Ha: u#3.3 E. Ho: µs3.3 Ha: µ> 3.3 F. Но: > 3.3 Ha: us3.3 (b) Identify the standardized test statistic, z. (Round to two decimal places as needed.) (c) Find the P-value. Hint: Keep in mind that P-value depends on the type of test. Left-tailed test: P-value=Area (where Area = the number from the table) Right-tailed test: P-value=1-Area Two-tailed test: P-value=2*Area P-value = (Round to three decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. Compare P with a and then State your conclusion. O A. Fail to reject Ho. There is not…The following table consists of one student athlete's time, x, (in minutes) to swim 2,500 yards and the student's heart rate, y, (beats per minute) after swimming on a random sample of 5 days: Athlete's Time (x) Heart Rate (y) x2 y? ху 33.43 145 34.89 150 35.12 125 37.27 143 36.56 138 ТОTAL 1. Compute for the value of Pearson's r. 2. Interpret the value of r.Suppose there is a claim that a certain population has a mean, u, that is greater than 8. You want to test this claim. To do so, you collect a large random sample from the population and perform a hypothesis test at the 0.05 level of significance. To start this test, you write the null hypothesis, Ho, and the alternative hypothesis, H₁, as follows. Ho: μ = 8 H₁: μ>8 Suppose you also know the following information. The value of the test statistic based on the sample is 1.717 (rounded to 3 decimal places). The p-value is 0.043 (rounded to 3 decimal places). (a) Complete the steps below for this hypothesis test. Standard Normal Distribution Step 1: Select one-tailed or two-tailed. One-tailed Two-tailed Step 2: Enter the test statistic. (Round to 3 decimal places.) Step 3: Shade the area represented by the p-value. Step 4: Enter the p-value. (Round to 3 decimal places.) 0.3 0.2 + 0.1 (b) Based on your answer to part (a), which statement below is true? O Since the p-value is less than (or…