a) What is the mean of Y? b) What are the degrees of freedom for the test? c) What is r?
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- A masking tape manufacturer expects 0.04 flaws per meter of tape, on average. The Poisson assumptions hold. Find the probability of exactly 1 flaw in 0.1 meters of tape. 0.0138 0.0289 0.0103 0.0221 0.0040An experimenter is interested in the hypothesis testing problemH0 : µ = 373 vs µ 6= 373where µ is the average breaking strength of a bundle of wool fibers. Suppose that a sampleof n = 29 wool fiber bundles is obtained and their breaking strengths are measured.(a) For what values of the t-statistic does the experimenter accept the null hypothesis with asize α = 0.10?(b) For what values of the t-statistic does the experimenter reject the null hypothesis with asize α = 0.01?Suppose that the sample mean is ¯x = 312.7 and the sample standard deviation is s = 8.13.(a) Is the null hypothesis accepted or rejected with α = 0.10? With α = 0.01?(b) Write down an expression for the p-value and evaluate it using a computer package.In quality–control applications of hypothesis testing, the null and alternative hypotheses are frequently specified as H0: The production process is performing satisfactorily and Ha: The process is performing in an unsatisfactory manner. Accordingly, α is sometimes referred to as the producer's risk, while β is called the consumer's risk. An injection molder produces plastic golf tees with a mean weight of 0.252 ounce. To investigate whether the injection molder is operating satisfactorily, 40 tees were randomly sampled from the last hour's production. Their weights (in ounces) are listed in the accompanying table. Complete parts a through g. 0.248 0.251 0.249 0.250 0.255 0.251 0.251 0.248 0.248 0.251 0.254 0.252 0.256 0.251 0.252 0.253 0.250 0.254 0.254 0.254 0.251 0.251 0.252 0.249 0.249 0.251 0.252 0.253 0.248 0.252 0.252 0.252 0.249 0.252 0.249 0.253 0.252 0.249 0.249 0.251 b.…
- In quality–control applications of hypothesis testing, the null and alternative hypotheses are frequently specified as H0: The production process is performing satisfactorily and Ha: The process is performing in an unsatisfactory manner. Accordingly, α is sometimes referred to as the producer's risk, while β is called the consumer's risk. An injection molder produces plastic golf tees with a mean weight of 0.252 ounce. To investigate whether the injection molder is operating satisfactorily, 40 tees were randomly sampled from the last hour's production. Their weights (in ounces) are listed in the accompanying table a. Write H0 and Ha in terms of the true mean weight of the golf tees, μ. A. H0: μ=0.252 Ha: μ<0.252 B. H0: μ=0.252 Ha: μ≠0.252 C. H0: μ=0.252 Ha: μ>0.252 D. H0: μ≠0.252 Ha: μ=A researcher is using a two-tailed hypothesis test with α = 0.05 to evaluate the effect of a treatment. If the boundaries for the critical region are t = ± 2.080, then how many individuals are in the sample?Suppose that a researcher decides that he MUST obtain a Type 1 error level of no more than 0.01 in order to reject the null hypothesis. After analyzing his data he finds that the results are significant at p = 0.05 but not at p = 0.01. If he is not able to change the maximum allowed Type 1 error level, then the researcher should Question 5 options: retain the null hypothesis because 0.05 is greater than 0.01. retain the null hypothesis because 0.05 is merely sampling error. reject the null hypothesis because 0.05 is close to 0.01. reject the null hypothesis because 0.05 is greater than 0.01.
- Q.6.1 A national publishing house claims that 37% of all weekly magazine readers in South Africa read their publication. Test this claim at the 1% significance level, if a survey found that 140 out of a random sample of 400 magazine readers said that they read the relevant publication. Q.6.2 The CEO of a large financial institution claims that, on average, their clients invest more than R45 000 per year in a particular portfolio. Test this claim at the 5% significance level if it was found that a sample of 21 clients invested an average of R44 500 in the portfolio over the last year, with a standard deviation of R5 500.A random sample of n1 = 14 winter days in Denver gave a sample mean pollution index x1 = 43. Previous studies show that σ1 = 19. For Englewood (a suburb of Denver), a random sample of n2 = 12 winter days gave a sample mean pollution index of x2 = 37. Previous studies show that σ2 = 13. Assume the pollution index is normally distributed in both Englewood and Denver. (a) State the null and alternate hypotheses. H0: μ1 = μ2; H1: μ1 > μ2 H0: μ1 < μ2; H1: μ1 = μ2 H0: μ1 = μ2; H1: μ1 < μ2 H0: μ1 = μ2; H1: μ1 ≠ μ2 (b) What sampling distribution will you use? What assumptions are you making? 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 unknown standard deviations. The standard normal. We assume that both population distributions are approximately normal with known standard deviations. The Student's t. We…a:- Show that the significant value of t at level of significance h for one-tailed test is equal to that of t at 2h significance level for two-tailed test. b:- It is a common experience that the volatility ( measured in terms of variance) of a financial market strategy is less than 0.25. Define the null and alternative hypothesis for testyyour faith oj this strategy.Perform a test at 1% level of significance to check the precision of a good undergoing this strategy.Following are the prices (in ruppes) of a particular good:. 2.9, 3.1, 3.2, 2.8, 2.7, 3.4, 2.6, 3.0, 3.3, 2.9, 2.8, 3.5
- 1a) Derive a maximum-liklihood estimator for the unknown parameter Y 1b) An experienced sales person completes sales following a Poisson distribution, with a mean rate of Y = 1.8 sales/month. A junior sales person completes sales at a mean rate of Y = 0.85 sales per month Find the probability of the joint sales team (experienced and junior) completing exactly 2 sales in any given months, assuming the two sales people act independently of each other. 1c) Find the probability of the joint sales team (experienced and junior) completing more than 2 sales in any given monthsThe worldwide market share for a web browser was 20.1% in a recent month. Suppose that a sample of 200 random students at a certain university finds that 50 use the browser. At the 0.01 level of significance, is there evidence that the market share for the web browser at the university is greater than the worldwide market share of 20.1%? Determine the null and alternative hypotheses. A.H0: P≥0.201; H1: P<0.201 B.H0: P=0.201; H1: P≠0.201 C. H0: P≠0.201; H1: P=0.201 D. H0: P≤0.201; H1: P>0.201 ZStat=__ (Round to two decimal places) p-value=____ __A__ the null hypothesis. There is __B__ evidence to conclude that the market share at teh university is __C__ the worldwide market share of 20.1%. A: Reject or do not reject B: insufficient or sufficient C: at least, less than, equal to, at most, not equal to, greater thanThe repair times of smart phones in a repair shop are independentrandom variables with the same mean and variance. The mean is 1 hour and thevariance is 0.2 hours. Obtain the approximate probability that 400 smart phonescan be repaired in less than 395 hours.I have to use the Central Limit Theorem to answer this question