The desired percentage of Sio, in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samplesare analyzed. Suppose that the percentage of Sio, in a sample is normally distributed with o = 0.32 and that x = 5.22. (Use a = 0.05.)(a) Does this indicate conclusively that the true average percentage differs from 5.5?State the appropriate null and alternative hypotheses.OHo: H = 5.5Hi H< 5.5O Ho: µ = 5.5Hai H2 5.5Ο H0: μ 5.5На: и# 5.5O Ho: H = 5.5Ha: u > 5.5Calculate 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-valueState the conclusion in the problem context.Reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage.Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage.Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage differs from the desired percentage.Reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage differs from the desired percentage.(b) If the true average percentage is u =5.6 and a level a = 0.01 test based on n = 16 is used, what is the probability of detecting this departure from Ho? (Round your answer to four decimalplaces.)(c) What value of n is required to satisfy a = 0.01 and B(5.6) = 0.01? (Round your answer up to the next whole number.)n =samples

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A survey of 90 recently delivered women on the rolls of a county welfare department revealed that 27 had a history of intrapartum or postpartum infection. What is the critical value of z if we need to conclude that the population proportion with a history of intrapartum or postpartum infection is less than 0.25.
The desired percentage of SiO2 in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO2 in a sample is normally distributed with σ = .3. Assume that the sample mean is 5.25. (a) Does this indicate that the true average percentage differs from 5.5? Carry out a test at α = .01. (b) If the true average percentage is µ = 5.6, what is the probability of type II error?
In an Omani factory, a machine that produces "W-product" has been set so that the true average diameter of the "W-product" it produces is 0.602 in. If its diameter is within 0.04 in. of this target value, this is acceptable. Suppose, however, that the setting has changed during the course of production, so that the products have normally distributed diameters with mean value 0.601 in. and standard deviation 0.002 in. What percentage of the "W-product" produced will not be acceptable
Suppose that samples of polythene bags from two manufacturers A and B are tested by a prospective buyer for bursting pressure, with the following results: If the prices are the same, which manufacture’s bags would be preferred by the buyer? Why?
As we have noted in previous chapters, even a very small effect can be significant if the sample is large enough. Suppose, for example, that a researcher obtains a correlation (computed from the raw data) of r = 0.60 for a sample of n = 10 participants. (4 pts. total) Is this sample sufficient to conclude that a significant correlation exists in the population? Use a two-tailed test with α = .05. In your response, be sure to specify the critical value for r.
A nationwide study of undergraduate students reported that the mean number of drinks consumed per week during the spring semester is 7.96. The mean number of drinks consumed per week at USC is 7.64 (s.d.=2.55, N=412 Health services is concerned that USC students are consuming significantly more alcohol per week than the national average. Using an alpha level of .05, Is there sufficient evidence to be concerned? Be sure to select the correct critical value for the alternative hypothesis, and then use this evidence to make your conclusion
Serum nitrite concentrations (in μmol/L) were compared between a group of unmedicated HIV+ subjects (n =7) and a control group (n = 10). The HIV+ distribution is strongly skewed.a) Use a Wilcoxon-Mann-Whitney U test to determine if there is convincing evidence at α = 0.05 thatserum nitrite levels differ between the two populations. b) What would have been the U test p-value if researchers had instead hypothesized that serum nitriteconcentrations would tend to be larger in the HIV+ population? HIV+ Control 0.266 0.167 0.269 0.201 0.299 0.205 0.335 0.232 0.503 0.234 0.846 0.260 0.946 0.268 0.288 0.301 0.305
Serum nitrite concentrations (in μmol/L) were compared between a group of unmedicated HIV+ subjects (n =7) and a control group (n = 10). The HIV+ distribution is strongly skewed. a) Use a Wilcoxon-Mann-Whitney U test to determine if there is convincing evidence at α = 0.05 thatserum nitrite levels differ between the two populations. b) What would have been the U test p-value if researchers had instead hypothesized that serum nitriteconcentrations would tend to be larger in the HIV+ population?
Records for the last 15 years have shown that the average rainfall in a certain region of the country, for the month of March, to be 1.20 inches, with s = 0.45 inches. A second region had an average rainfall of 1.35 inches, with s = 0.54. estimate the difference of the true average rainfalls in those two regions as a 95% C.I. with the assumption of normal populations and unequal variances.
In response to concerns about nutritional contents of fast foods, McDonald’s announced that it would use a new cooking oil for its french fries that would decrease substantially trans fatty acid levels and increase the amount of more beneficial poly-unsaturated fat. The company claimed that 97 out of 100 people cannot detect a difference in taste between the new and old oils. Assuming that this figure is correct (as a long-run proportion). Let X denote the number of individuals who can taste the difference between the two oils in a random sample of 1000 individuals who have purchased fries at McDonald’s. If it turns out that 65 individuals in the sample can taste the difference between the two oils, would you question McDonald’s claim? Explain why or why not.
In response to concerns about the nutritional contents of fast foods, McDonald’s announced that it would use new cooking oil for its french fries that would decrease substantially trans fatty acid levels and increase the amount of more beneficial poly-unsaturated fat. The company claimed that 97 out of 100 people cannot detect a difference in taste between the new and old oils. Assuming that this figure is correct (as a long-run proportion). Let X denote the number of individuals who can taste the difference between the two oils in a random sample of 1000 individuals who have purchased fries at McDonald’s. Use the normal approximation with continuity correction to find the probability that at most 5% can taste the difference between the two oils.
Assume that last year in a particular state with 700000 children there were 1471 children out of 32500 in a random sample who were diagnosed with Autism Spectrum Disorder. Nationally, 1 out of 88 children are diagnosed with ASD. Is there sufficient data to show that the incident rate of ASD is higher in that state than nationally? Test at the 1% level.

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