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- The sample mean and standard deviation from a random sample of 30 observations from a normal population were computed as x¯=31x¯=31 and s = 9. Calculate the t statistic of the test required to determine whether there is enough evidence to infer at the 3% significance level that the population mean is greater than 28. Test Statistic =In a test of HO; u = 80 against HA,: u z 80, a sample of observations had a mean X = 78 and standard deviation s = 4.1. Find the p-value for the test. Compute it manually, not excel.The sample mean and standard deviation from a random sample of 29 observations from a normal population were computed as ?¯=23x¯=23 and s = 6. Calculate the t statistic of the test required to determine whether there is enough evidence to infer that the population mean is greater than 21. Test Statistic =
- A sample of n=49 scores is selected from a normal population with a mean of u=60 and a standard deviation of o=12. The probability that the selected mean will be greater than m=63 is equal to the probability of obtaining a z score greater than z= +1.75Find the P-value for a right-tailed test about a mean with n = 36 and test statistic t = 46.2766 at 90% confidence level. cannot be computed higher than 0.05 equal to 0.05 less than 0.05Assume that the readings at freezing on a bundle of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested.If 4.8% of the thermometers are rejected because they have readings that are too high and another 4.8% are rejected because they have readings that are too low, find the two readings that are cutoff values separating the rejected thermometers from the others.interval of acceptable thermometer readings =_____________ °C
- Suppose the lengths of human pregnancies are normally distributed with u = 266 days and 0 = 16 days. The area to the left of X = 245 is 0.0947. What is the probability that a randomly selected human pregnancy lastsAn entire population has mean of μ = 17.4 andstandard deviation of σ = 3.2.By using Chebyshev’s Theorem, determine the least percentage of the population of X,whose value is between 13.7 and 25.2A random sample of n = 16 scores is obtained from a population with a mean of u ment is administered to the individuals in the sample, the sample mean is found to be M = 49.2. a. Assuming that the sample standard deviation is s = 8, compute r and the estimated Cohen's d to measure the size of the treatment effect. %3D 45. After a treat- b. Assuming that the sample standard deviation is s = 20, compute r and the estimated Cohen's d to measure the size of the treatment effect. c. Comparing your answers from parts a and b, how does the variability of the scores in the sample influence theneasures of effect size?
- 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 ? = 0.32 and that x = 5.21. (Use ? = 0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5?State the appropriate null and alternative hypotheses. H0: ? = 5.5Ha: ? ≠ 5.5H0: ? = 5.5Ha: ? ≥ 5.5 H0: ? = 5.5Ha: ? < 5.5H0: ? = 5.5Ha: ? > 5.5 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 = State the conclusion in the problem context. Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage.Reject the null hypothesis. There is sufficient evidence…Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested.If 4.7% of the thermometers are rejected because they have readings that are too high and another 4.7% are rejected because they have readings that are too low, find the two readings that are cutoff values separating the rejected thermometers from the others.Interval of acceptable thermometer readings _________ °CEnter your answer as an interval (a,b) with 2-decimal place accuracy.Suppose that the heights of adult females is normally distibuted with population mean equal to 168cm and population standard deviation equal to 6cm. Let X denote the height of a randomly individual fro the population of adult females d) What is the probabaility that X is in between 166cccm and 172cm? e) Suppose a smaple of 20 individuals are randomly selected from population of adult females. Let x̄ denote the mean height of this random sammple of adult females i) What is the distribution of x̄ in conventional statistical notation? ii)What is the probability that x̄ is in between 166.5 cm and 171.5cm?