You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=30.1σ=30.1. You would like to be 99% confident that your estimate is within 4 of the true population mean. How large of a sample size is required? n = Do not round mid-calculation. However, you are encouraged to use a critical value accurate to three decimal places — this is important for the system to be able to give hints for incorrect answers.
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n =
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- A scientist studying local lakes claims that there is a linear relationship between a lake’s level of mercury and the lake’s depth. The scientist collected data to test the claim at a significance level of α=0.01. The following hypotheses were tested. H0:β1=0Ha:β1≠0 The test yielded a t-value of 2.7 and a p-value of 0.012. Which of the following is a correct conclusion about the scientist’s claim? The null hypothesis is rejected since 0.012>0.01. There is sufficient evidence to suggest that there is a linear relationship between a lake’s level of mercury and the lake’s depth. A The null hypothesis is not rejected since 0.012>0.01. There is sufficient evidence to suggest that there is a linear relationship between a lake’s level of mercury and the lake’s depth. B The null hypothesis is rejected since 0.012>0.01. There is not sufficient evidence to suggest that there is a linear relationship between a lake’s level of mercury and the lake’s depth.…Life-saving drug: Penicillin is produced by the Penicillin fungus, which is grown in a broth whose sugar content must be carefully controlled. Several samples of broth were taken on three successive days, and the amount of dissolved sugars, in milligrams per milliliter, was measured on each sample. The results were as follows. Day 1: 5.2 5.0 5.4 5.2 5.3 5.0 4.9 5.0 5.2 5.0 4.6 5.3 Day 2: 5.6 4.8 4.9 5.3 5.2 4.9 5.4 5.0 5.4 4.9 5.5 5.4 Day 3: 5.9 4.9 5.3 5.4 5.2 5.5 5.0 5.8 5.5 5.4 5.4 5.1 Construct an ANOVA table. Round your answers to four decimal places as needed. One-way ANOVA: Sugar Concentration Source DF SS MS F P Days Error TotalA random sample of 54 students from Cabrillo College are selected from a normal population with mu equal to 20 and sigma equal to 5. After a treatment is administered to the students, the researcher calculated the sample mean to be 21. Is there enough evidence to conclude that the treatment had an effect at the 5% significance level? In step three, can we use the Critical Value Method? (a)Don't know (b)Cannot Determine (c)No (d)Yes
- A random sample of size 15 taken from a normally distributed population resulted in a sample variance of 32 and a sample mean of 50. The lower limit of a 90% confidence interval for the population variance would be? Formula: E=tα/2(s/√n). In general, a ____ t-statistic and a _____ p-value (relative to a chosen critical value and alpha) indicate that our estimated statistic is ____ to occur by chance if the null is true. a. Large; large; likely b. Small; large; likely c. Small; small; unlikely d. Large; large; likelySuppose a variable is Normally distributed with μ=345 and sigma σ=30. What proportion of the data has values below 350? Use four decimal places in your answer. Suppose a variable is Normally distributed with μ=345 and sigma σ=30. What proportion of the data has values above 390? Use four decimal places in your answer. Suppose a variable is Normally distributed with μ=345 and sigma σ=30. What proportion of the data has values between 330 and 345? Use four decimal places in your answer.
- Stock y has a beta of 1.2 and an expected return of 11.5. Stock z has a beta of .80 and an expected return of 8.5 percentArsenic-based additives in chicken feed have been banned by the European Union. Ifa restaurant chain finds significant evidence that the mean arsenic level of theirchickens is above 80 ppb (parts per billion), the chain will stop using that supplier ofchicken meat. The hypotheses are: H 0 : µ = 80H 1 : µ > 80 where µ represents the mean arsenic level in all chicken meat from that supplier.Samples from two different suppliers are analyzed, and the resulting p-values aregiven: Sample from Supplier A: p-value is 0.0003Sample from Supplier B: p-value is 0.3500 a) Interpret each p-value in terms of the probability of the results happening byrandom chance. b) Which p-value shows stronger evidence for the alternative hypothesis? c) Which supplier, A or B, should the chain get chickens from in order to avoid toohigh a level of arsenic?In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below. PatientsCured PatientsNot Cured Received medication 80 10 Received sugar pills 20 50 We are interested in determining whether or not the medication was effective in curing the common cold. The hypothesis is to be tested at the 10% level of significance. The critical value from the table equals a. 2.706 b. 3.841 c. 7.81 d. 5.99
- You need to test whether the average mealtime spending of American tourists (population 1) is greater than that for British tourists (population 2). Assume that you have a sample of n1=7 with sample mean X1=40 and a sample standard deviation of S1=6, and you have an independent sample of n2=16 from another population with a sample mean of X2=31 and sample standard deviation S2=5. Complete parts (a) to (d). Click here to view page 1 of the table of the critical values of t. LOADING... Click here to view page 2 of the table of the critical values of t. LOADING... a. What is the value of the pooled-variance t test statistic for testing? t=enter your response here (Type an integer or a decimal rounded to two decimal places as needed.) b. In finding the critical value of the test statistic t, how many degrees of freedom are there? There are enter your response here degrees of freedom. c. Using a significance level of α=0.01, what is the critical value for a…Betty, an employee of Shining Sun Daycare Centerread an article in Healthy Child Magazine sayingthat the average 3-year-old child is 37 in. tall.Betty works with 10 3-year-olds at Shining Sun,so later that week, she measured the height ofeach child who had just turned or was about toturn 3 years old. Here are the descriptive statisticsfor the sample: M = 35, s = 3.1. State the nondirectional hypothesis.2. Determine the critical t for a = .05.3. Calculate t. Show your calculations.4. Is the height of 3-year-olds in Shining SunDaycare Center significantly different fromthe height given in the magazine?A) What is the t critical value? B) What is the t statistic value? C) True or False. We fail to reject the null hypothesis and that means the tuning forks are not significantly out of tune.