An agronomist examines the cellulose content of a variety of alfalfa hay. Suppose that the cellulose content in the population has standard deviation ? = 9 milligrams per gram (mg/g). A sample of 15 cuttings has mean cellulose content x = 145 mg/g. (a) Give a 90% confidence interval for the mean cellulose content in the population. (Round your answers to two decimal places.) , (b) A previous study claimed that the mean cellulose content was ? = 140 mg/g, but the agronomist believes that the mean is higher than that figure. State H0 and Ha. H0: ? > 140 mg/g; Ha: ? = 140 mg/g H0: ? = 140 mg/g; Ha: ? > 140 mg/g H0: ? = 140 mg/g; Ha: ? ? 140 mg/g H0: ? = 140 mg/g; Ha: ? < 140 mg/g H0: ? < 140 mg/g; Ha: ? = 140 mg/g Carry out a significance test to see if the new data support this belief. (Use ? = 0.05. Round your value for z to two decimal places and round your P-value to four decimal places.) z = P-value = Do the data support this belief? State your conclusion. Reject the null hypothesis, there is significant evidence of a mean cellulose content greater than 140 mg/g. Reject the null hypothesis, there not is significant evidence of a mean cellulose content greater than 140 mg/g. Fail to reject the null hypothesis, there is significant evidence of a mean cellulose content greater than 140 mg/g. Fail to reject the null hypothesis, there not is significant evidence of a mean cellulose content greater than 140 mg/g. (c) The statistical procedures used in (a) and (b) are valid when several assumptions are met. What are these assumptions? (Select all that apply.) We must assume that the 15 cuttings in our sample are an SRS. We must assume that the sample has an underlying distribution that is uniform. Because our sample is not too large, the population should be normally distributed, or at least not extremely nonnormal. Because our sample is not too large, the standard deviation of the population and sample must be less than 10.
An agronomist examines the cellulose content of a variety of alfalfa hay. Suppose that the cellulose...
A study of iron deficiency among infants compared samples of infants following different feeding regimens. One group contained breast-fed infants, while the infants in another group were fed a standard baby formula without any iron supplements. Here are summary results on blood hemoglobin levels at 12 months of age. Group n x s Breast-fed 22 13.3 1.6 Formula 20 12.7 1.7 (a) Is there significant evidence that the mean hemoglobin level is higher among breast-fed babies? State H0 and Ha....
A nutrition lab tested 40 hot dogs to see if their mean sodium content was less than the 325-mg upper limit set by regulations for "reduced sodium" franks. The mean sodium content for the sample was 322.3 mg with a standard deviation of 17 mg. Assume that the assumptions and conditions for the test are met. a) Test the hypothesis that the mean sodium content meets the regulation. b) Will a larger sample size ensure that the regulations are met?...
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Suppose you wish to conduct a test of the research hypothesis that the median of a population is greater than 73. You randomly sample 20 measurements from the population and determine that 13 of them exceed 73. Set up and conduct thee appropriate test of hypothesis at the 0.10 level of significance. Be sure to specify all necessary assumptions. What are the null and alternative hypotheses for this hypothesis tast? OA. Ho: n-13 He :...
A nutrition lab tested 40 hot dogs to see if their mean sodium content was less than the 325-mg upper limit set by regulations for "reduced sodium" franks. The mean sodium content for the sample was 321.6 mg with a standard deviation of 19 mg. Choose the appropriate null and alternative hypotheses A. H0: u=325 HA: u<325 B. H0: u=325 HA: u=321.6 C. H0: u=325 HA: u does not equal 325 (its the equal sign with a slash in it)...
Two proposed computer mouse designs were compared by recording wrist extension in degrees for 24 people who each used both mouse designs.† The difference in wrist extension was calculated by subtracting extension for mouse type B from the wrist extension for mouse type A for each person. The mean difference was reported to be 8.82 degrees. Assume that this sample of 24 people is representative of the population of computer users. (a) Suppose that the standard deviation of the differences...
Two proposed computer mouse designs were compared by recording wrist extension in degrees for 24 people who each used both mouse designs.† The difference in wrist extension was calculated by subtracting extension for mouse type B from the wrist extension for mouse type A for each person. The mean difference was reported to be 8.82 degrees. Assume that this sample of 24 people is representative of the population of computer users. (a) Suppose that the standard deviation of the differences...
Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna).† Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows. 3.7 2.9 3.8 4.2 4.8 3.1 The sample mean is x = 3.75 grams. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution...
A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is 40 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty 12-ounce bottles of cola has a mean caffeine content of 40.9 milligrams. Assume the population is normally distributed and the population standard deviation is 7.9 milligrams. At x=0.04, can you reject the company's claim? Complete parts (a) through (e). A. Identify Upper H0...
A sample of size 100, taken from a population whose standard deviation is known to be 8.90, has a sample mean of 51.16. Suppose that we have adopted the null hypothesis that the actual population mean is greater than or equal to 52, that is, H0 is that μ ≥ 52 and we want to test the alternative hypothesis, H1, that μ < 52, with level of significance α = 0.05. a) What type of test would be appropriate in...
For a random sample of 36 data pairs, the sample mean of the differences was 0.72. The sample standard deviation of the differences was 2. At the 5% level of significance, test the claim that the population mean of the differences is different from 0. (a) Is it appropriate to use a Student's t distribution for the sample test statistic? Explain. No, the sample size is not larger than 30. Yes, the sample size is larger than 30. No, the...