Example 1 Does y = e* - 2 exist? What is the domain & range of the function ifit does exist? (show full working out)
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- A local chess club claims that the length of time to play a game has a mean of 43 minutes or more. Write sentences describing type I and type II errors for a hypothesis test of this claim. A type I error will occur if the actual mean of the length of time to play a game is ▼ equal to less than or equal to not equal to greater than or equal to greater than less than 43 minutes, but you ▼ reject fail to reject the null hypothesis, ▼ Upper H 0 : mu greater than or equals 43H0: μ≥43 Upper H 0 : mu not equals 43H0: μ≠43 Upper H 0 : mu equals 43H0: μ=43 Upper H 0 : mu less than or equals 43H0: μ≤43 Upper H 0 : mu greater than 43H0: μ>43 Upper H 0 : mu less than 43H0: μ<43 . A type II error will occur if the actual mean of the length of time to play a game is ▼ greater than less than or equal to less than greater than or equal to equal to not equal to 43 minutes, but you ▼ fail to reject reject the null hypothesis, ▼ Upper H 0…Find kurtosis by using ungroup data given in the picture using quartile deviation, make sure to arrange data before solving question.The probability that the Air Conditioning of a brand new car is defective is 10%. Let X be the number of cars with defective AC in a sample of size 100. (a). Find P(X < 6) exactly. (b). ) Find P(X < 6) approximately, using a Poisson approximation (c). Find P(X < 6) approximately, using a normal approximation. Note: For parts (a) and (b), you only need to provide a formal expression each. For part (c), you need to compute the numerical values using the Q-function table (Table 4.2) from the textbook.
- A common characterization of obese individuals is that their body mass index is at least 30 [BMI = weight/(height)2, where height is in meters and weight is in kilograms]. An article reported that in a sample of female workers, 269 had BMIs of less than 25, 156 had BMIs that were at least 25 but less than 30, and 121 had BMIs exceeding 30. Is there compelling evidence for concluding that more than 20% of the individuals in the sampled population are obese? (a) State the appropriate hypotheses with a significance level of 0.05. H0: p = 0.20Ha: p > 0.20H0: p > 0.20Ha: p = 0.20 H0: p = 0.20Ha: p < 0.20H0: p = 0.20Ha: p ≠ 0.20 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z=P-value= What can you conclude? Reject the null hypothesis. There is sufficient evidence that more than 20% of the population of female workers is obese.Reject the null hypothesis. There is not…A researcher is testing the effect of a new cold and flu medication on reaction time. A sample of n = 16 students is obtained and each student is given the normal dose of the medicine. Thirty minutes later, each student's reaction time is measured. The scores for the sample averaged M = 220 milliseconds with SS = 6000. Assuming that reaction time for students in the regular population averages μ = 200 milliseconds, are the data sufficient to conclude that the medication has a significant effect on reaction time? Test at the .05 level of significance. Make a point estimate and a 95% confidence interval estimate for the treated population mean.Suppose we want to compare the length of hospital stay for patients with the same diagnosis at two different hospitals. The results are shown in Table 9.10. 9.7 Why might a t test not be very useful in this case? 9.8 Carry out a nonparametric procedure for testing the hypothesis that lengths of stay are comparable in the two hospitals.
- A pharmcuticle company claims that its new drug reduces systolic blood pressure. The systolic blood pressure (in millimeters of Mercury) for 9 patients before taking the new drug and 2 hours after taking the drug are shown in the table below. is there enough evidence support the company's claim? Let D =(blood pressure before taking new drug)- (blood pressure after taking new drug).use significant levels of a=their 0.05 for the test. Assume that the systolic blood pressure levels are normally distributed for the population of patience both Before & After taking the new drug. 1.State the null and alternative hypothesis for the test. 2. Find the value of the standard deviation of the paired differences. Round to one decimal place. 3.compute the value of the test statistic. Round to three decimal places 4.determine the decision rule for rejecting the null hypothesis Ho. Round the numerical portion to three decimals. 5.make decision for the hypothesis test.The germination rate of seeds is defined as the proportion of seeds that, when properly planted and watered, sprout and grow. A certain variety of grass seed usually has a germination rate of 0.80, and a company wants to see if spraying the seeds with a chemical that is known to change germination rates in other species will change the germination rate of this grass species. (a) Suppose the company plans to spray a random sample of 400 seeds and conduct a two-sided test of 0: 0.8Hpusing = 0.05. They determine that the power of this test against the alternative 0.75pis 0.69. Interpret the power of this test.(b) Describe two ways the company can increase the power of the test. What is a disadvantage of each of these ways? (c) The company researchers spray 400 seeds with the chemical and 307 of the seeds germinate. This produces a 95% confidence interval for the proportion of seeds that germinate of (0.726, 0.809). Use this confidence interval to determine whether the test described in…A mutation in Gene A is thought to be associated with a disease. The mutation in Gene A is found in 5% of the population. 2% of the whole population is diagnosed with disease B at some point in their life time. 1% of the population both has the mutation and also gets diagnosed with the disease in their life time. Is the provided data adequate to test the independency of mutation in Gene A and occurrence of Disease B? If it is not, what other information or data is needed to test the independency? What is the probability of Disease B, among the individuals with the mutation in Gene A? What is the probability of having the mutation in Gene A among the individuals with Disease B? If an individual has the mutated Gene A, what is their Relative Risk of developing the disease?
- A congressional committee is composed of 10 members: 6 Republicans and 4 Democrats. On any given vote, members vote independently. Whereas Republicans always vote their party line, Democrats vote their party line with probability .8, and vote Republican with probability .2. On a rainy day only 3 committee members (selected w/o replacement) were present. Let X = number of Democrats present Y = Number who voted Democratic that day Find the marginal pdf of X, i.e., P[X=k] for k=0, 1, 2, 3. Display E[X] and VAR[X]. Determine the conditional probability that P[ Y=j | X=k] for k=3 and j=0,1,2,3 Display the table of joint probabilities fX,Y(i,j) for 0 ≤ j ≤ i, i=0,1,2,3 Display the marginal pdf of Y. Is it recognizable? Compute E[Y]and VAR[Y]. Determine the conditional expectation of Y given that X=x, for x=0,1,2,3.…: The following table reports the results of a t-test using STATA.Group 1 refers to developed countries, Group 0 refers to the off-shores andEuropean & Asian developing countries. The statistics reported are based on theaverage liquid liabilities during the 2000s.i. Carefully set up the null and alternative hypothesis, the risk you encounterin your decision, the steps to make the decision, and provide a clearconclusion using the p-value.ii. Using the t-values draw a graph showing the corresponding values of the tand the acceptance and rejection areas.iii. A friend believes that your decision was a Type I error. Explains what itmeans.iv. Using information provided in the STATA output above, show how the tstatistic for the test has been calculated.v. Using the information provided in the table above, show how the 95%confidence intervals have been derived. Also calculate and comment on theconfidence interval at 99%, explaining what the confidence intervalscapture.The average drying time of a manufacturer’s paint is 20 minutes. Investigating the effectiveness of a modifica-tion in the chemical composition of her paint, the manu-facturer wants to test the null hypothesis μ = 20 minutes against a suitable alternative, where μ is the average dry-ing time of the modified paint. (a) What alternative hypothesis should the manufactureruse if she does not want to make the modification in thechemical composition of the paint unless it decreases thedrying time?(b) What alternative hypothesis should the manufactureruse if the new process is actually cheaper and she wants tomake the modification unless it increases the drying timeof the paint?