TF.16 A random sample of size 50 is used to test the null hypothesis H0 : μ = 5.5 (the average monthly salary in thousands of dollars ($5,500) for new assistant professors) against Ha : μ > 5.5. The sample mean is x̄ = 5.75, and the population standard deviation is σ = 0.85. Test H0 against Ha at α = 0.01 level of significance. Find the p-value.
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- The nicotine content in cigarettes of a certain brand is normally distributed. The brand advertises that the mean nicotine content of their cigarettes is µ = 1.5, but measurements on a random sample of 100 cigarettes of this brand gave a mean of ?̅= 1.53 and s = 0.95. Is this evidence that the mean nicotine content is actually higher than advertised? 1. State the appropriate null and alternative hypotheses. H0: ? = 1.5 Ha: ? > 1.5 2. Should you use the z or t test? t – do not have sigma 3. Compute the test statistic to test your hypotheses. (report to 2 decimal places) ? = 1.53−1.5 0.95 √100 ⁄ = 0.32 4. Find the appropriate range of p-value for your test. P-value: a. Less than 0.005 b. Between 0.005 and 0.01 c. Between 0.01 and 0.025 d. Between 0.025 and 0.05 e. Greater than 0.05A nutritionist claims that the mean tuna consumption by a person is 3.3 pounds per year. A sample of 50 people shows that the mean tuna consumption by a person is 3.1 pounds per year. Assume the population standard deviation is 1.21 pounds. At α = 0.1, can you reject the claim? (a) Identify the null hypothesis and alternative hypothesis. A. Ho: μ#3.1 H₂:μ = 3.1 D. H₂:μ≤3.1 Ha:μ>3.1 (b) Identify the standardized test statistic. Z= (Round to two decimal places as needed.) B. Ho: μ = 3.3 H₂:μ#3.3 E. Ho:μ≤3.3 Ha:μ>3.3 C. Ho: μ>3.3 H₂:μ≤3.3 F. Ho: μ>3.1 Hg:μ≤3.1a. Report and interpret the P-value for Fisher's exact test with (i) Ha: 0 > 1 and (ii) Hạ: 0 # 1. Explain how the P-values are calculated. b. Find and interpret the mid P-value for Ha: 0 > 1. Summarize advantages and disadvantages of this type of P-value. Table 3.14 Data for Exercise 3.18 on Therapy for Cancer of Larynx Cancer Controlled Cancer Not Controlled Surgery Radiation therapy 21 15 23
- Let m denote margin of error, n sample size and σ standard deviation. m= zα/2(σn) Solve the above equation for n.You wish to test the claim Ha using a significance level of α=0.01. Ho:μ1=μ2 Ha:μ1≠μ2 You obtain a sample of size n1=28 with a mean of ¯x1=52.3 and a standard deviation of s1=13.7 from the first population. You obtain a sample of size n2=25 with a mean of ¯x2=42.1 and a standard deviation of s2=18.1 from the second population. Use the Theory-based inference applet to answer the following questions. (a) What is the t-score for this situation? Report your answer accurate to two decimal places. t-score = (b) What is the (theory-based) p-value for this situation? Report your answer accurate to four decimal places. p-value = (c) State a conclusion about the claim using a complete sentence.A sample obtained from a population with σ = 12 has a standard error of σx̅ = 2 points. How many scores are in the sample?
- To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B. The mean braking distance for Make A is 43 feet. Assume the population standard deviation is 4.6 feet. The mean braking distance for Make B is 46 feet. Assume the population standard deviation is 4.5 feet. At α=0.10, can the engineer support the claim that the mean braking distances are different for the two makes of automobiles? Assume the samples are random and independent, and the populations are normally distributed. The critical value(s) is/are Find the standardized test statistic z for μ1−μ2.Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P(Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P(A sample of n=25 scores has a mean of M=68. Find the z-score for this sample: If it was obtained from a population with m=60 and s=10. If it was obtained from a population with m=60 and s=20. If it was obtained from a population with m=60 and s=40. A normal distribution has a mean of μ = 54 and a standard deviation of σ = 6. What is the probability of randomly selecting a score less than X = 51? What is the probability of selecting a sample of n = 4 scores with a mean less than M = 51? What is the probability of selecting a sample of n = 36 scores with a mean less than M = 51? A sample is selected from a population with a mean of and a standard deviation of . If the sample has scores, what is the expected value of and the standard error of If the sample has scores, what is the expected value of and the standard error of ? A random sample is obtained from a normal population with a mean of and a standard deviation of . The sample mean is Is this a…A simple random sample of size n=40 is drawn from a population. The sample mean is found to be 107.6, and the sample standard deviation is found to be 20.2. Is the population mean greater than 100 at the α=0.025 level of significance? Determine the null and alternative hypotheses. H0: mu equals 100μ=100 mu less than 100μ<100 mu equals 100μ=100 mu greater than 100μ>100 mu less than 107.6μ<107.6 mu equals 107.6μ=107.6 mu greater than 107.6μ>107.6 H1: mu greater than 100μ>100 mu less than 100μ<100 mu equals 100μ=100 mu greater than 100μ>100 mu less than 107.6μ<107.6 mu equals 107.6μ=107.6 mu greater than 107.6μ>107.6 Compute the test statistic. t 0t0 t 0t0 z 0z0 = (Round to two decimal places as needed.) Determine the P-value. The P-value is . (Round to three decimal places as needed.) What is the result of the hypothesis test? the null hypothesis because the P-value is the level of significance.…ndependent random samples are selected from two populations and are used to test the hypothesis Hn: (H, - H2) = 0 against the alternative H,: (4, - H2) #0. An analysis of 232 observations from population 1 and 311 from population 2 yielded p-value of 0.113. Complete parts a and b below. a. Interpret the results of the computer analysis. Use as0.10. A. Since this p-value exceeds the given value of a, there is insufficient evidence to indicate that the population means are different. O B. Since the given a value exceeds this p-value, there is insufficient evidence to indicate that the population means are different. OC. Since the given a value exceeds this p-value, there sufficient evidence to indicate that the population means are different. O D. Since this p-value exceeds the given value of , there is sufficient evidence to indicate that the population means are different. b. If the alternative hypothesis had been Ha: (H1 - H2) <0, how would the p-value change? Interpret the p-value…Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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