(a). The null and alternative hypotheses are Но: 3D 21.7 Ha:µ > 21.7 Ho:µ = 20.3 Но: %| На: д < 20.3 Ο H0: μ =21.7 Ha:µ < 21.7 Ho :ã = 20.3 Ha:ã < 20.3
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- A biologist believes that there has been increase in the mean total suspended solids (TSS, mg/L) among Philippine rivers since its last study, where a mean 80 mg/L of TSS was observed. A random sample of 25 rivers was observed and the mean TSS was found to be 100 mg/L. Suppose it is of interest to test the biologist claim, the appropriate pair of null and alternative hypotheses is O Ho: µ-80, Ha: μ>80 O Ho: μ-100, Ha: µ>100 O Ho: X-bar = 80, Ha: X-bar > 80 O Ho: X-bar = 100, Ha: X-bar > 100FURC’s security officer set up the standard µ = 60 minutes and σ = 3.0minutes to complete the campus security round by a guard during the night duty. One day security officer observed that a guard hascompleted five rounds on average in 56 minutes. Set up a hypothesis and alternative hypothesis and perform the test at the 5% level.60% of students entering four-year colleges receive a degree within six years. Is this percent larger than for students who play intramural sports? 172 of the 249 students who played intramural sports received a degree within six years. What can be concluded at the level of significance of αα = 0.10? For this study, we should use (t-test, z-test) The null and alternative hypotheses would be: Ho: (symbol) (symbol) _____ (please enter a decimal) H1: (symbol) (symbol) _____ (Please enter a decimal) The test statistic (symbol) = _____ (please show your answer to 3 decimal places.) The p-value = _______ (Please show your answer to 4 decimal places.) The p-value is (symbol) αα Based on this, we should the null hypothesis. Thus, the final conclusion is that ... The data suggest the population proportion is not significantly larger than 60% at αα = 0.10, so there is sufficient evidence to conclude that the population proportion of students who…
- Past research has indicated that the average age of death row inmates is 41 years old. researcher would like to determine if the average age has changed. She randomly selects 50 death row inma s and ds their average age to be 37 years old. The hypothesis the statistician wants to test is: a. Ho: µ=37 vs_ Ha: µ ± 41. b. Ho: µ=41 vs Ha: µ< 41. Ho: u = 41 vs. H: u 41 d. Ho: µ=37 vs_Ha: µ< 41. C. 2. If a player at a casino is playing roulette and betting on red, there is a 18 / 38 or 0.474 chance that he will win on any spin of the roulette wheel. If we take a random sample of 300 players betting on red, then p is the proportion of times that the player wins. What is the mean of the sampling distribution of p? t' a. b. What is the standard deviation (os) of the sampling distribution of p? c. If repeated samples of 300 players are taken, what would be the range of the sample proportion of players victories according to the 95 part of the 68-95-99.7 rule" pts) 3. The z statistic for a…16% of all Americans suffer from sleep apnea. A researcher suspects that a lower percentage of those who live in the inner city have sleep apnea. Of the 398 people from the inner city surveyed, 52 of them suffered from sleep apnea. What can be concluded at the level of significance of αα = 0.01? For this study, we should use Z TEST FOR A POPULATION PROPORTION The null and alternative hypotheses would be: Ho: P=0.15 (please enter a decimal) H1: P <0.1 3. The test statistic _z__ = _______ (please show your answer to 3 decimal places.) 4. The p-value = __0.0144__ (Please show your answer to 4 decimal places.) 5. The p-value is __<__α 6. Based on this, we should ___FAIL TO REJECT___ the null hypothesis. Thus, the final conclusion is that ... The data suggest the populaton proportion is significantly smaller than 16% at αα = 0.01, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is…A demographer wants to measure life expectancy in countries 1 and 2. Let μ1 and μ2 denote the mean life expectancy in countries 1 and 2, respectively. Specify the hypothesis to determine if life expectancy in country 1 is more than 10 years lower than in country 2.
- A researcher suspects that the mean birth weights of babies whose mothers did not see a doctor before delivery is less than 3000 grams. The researcher states the hypotheses as H:x = 3000 grams H, x 3000 grams; He:x< 3000 grams, where x = the mean birth weights of the sample of babies whose mothers did not see a doctor before delivery. Ho: x < 3000 grams; H,:x = 3000 grams, where x = the mean birth weights of the sample of babies whose mothers did not see a doctor before delivery. Ho: = 3000 grams; H # 3000 grams, where = the true mean birth weights of all babies whose mothers did not see a doctor before delivery. Ho: i = 3000 grams; H:< 3000 grams, where = the true mean birth weights of all babies whose mothers did not see a doctor before delivery. O Ho : š == 3000 grams; H. x 3000 grams, where x = the mean birth weights of the sample of babies whose mothers did not see a doctor before delivery.10. A sample of high-capacity resistors is tested until failure and the results fitted to a Weibull probability model. Based on these tests, the reliability function of a resis- tor is estimated to be -0.0013 rl.83 R(1) = e' a. What is the failure rate function for these resistors? b. Is this resistor more likely to fail as it ages? c. What is the probability that a resistor will function for more than 30 hours with- out failure? d. Suppose that a resistor has been operating for 50 hours. What is the probability that it fails in the 5 1st hour? [Use the results of part (a) for your calculations.]The mean ±1 sd of ln [calcium intake (mg)] among 25 females, 12 to 14 years of age, below the poverty level is 6.56 ± 0.64. Similarly, the mean ± 1 sd of ln [calcium intake (mg)] among 40 females, 12 to 14 years of age, above the poverty level is 6.80 ± 0.76. *8.7 Suppose an equal number of 12- to 14-year-old girls below and above the poverty level are recruited to studydifferences in calcium intake. How many girls should be recruited to have an 80% chance of detecting a significant difference using a two-sided test with α = .05? *8.8 Answer Problem 8.7 if a one-sided rather than a twosided test is used. *8.9 Using a two-sided test with α = .05, answer Problem 8.7, anticipating that two girls above the poverty level will be recruited for every one girl below the poverty level who is recruited.
- Given the following information: P(A) = 0.4, P(B) = 0.3, P(C)= 0.5, P(AOB)= 0.12, P(BOC)= 0.13, P(AnC) = 0.11, P(A^BoC)=0.05. The value of P((Bn©)|Ā) is 20 13 15 41 49 41 6011. A hypothesis test is conducted with H0 : µ = 46 vs. Ha: µ ≠ 46. The hypothesis test sample finds x̅ = 47.2, s = 5, and n = 81. The tail area in this test is P =An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects prior to using the potatoes to make potato chips. Unless there is clear evidence that this proportion is less than 0.10, she will reject the shipment. To reach a decision, she will test the hypotheses Ho: p=0.10, Ha p<0.10 To do so, she selects an SRS of 150 potatoes from the more than 3000 potatoes on the truck. Suppose that six of the potatoes sampled are found to have major defects. Which of the following assumptions for inference about a proportion, using a hypothesis test, are violated? O The data are an SRS from the population of interest. O There appear to be no violations. O The population is at least 10 times as large as the sample. n is so large that both npo and n(1-Po) are 10 or more, where po is the proportion with major defects, if the null hypothesis is true.