3. A random sample of 25 observations taken from a population that is normally distributed produced a sample mean of 58.5 and a standard deviation of 7.5. Find the critical and observed values of t for each of the following tests of hypothesis using a = 0.01. a) H₂:μ = 55 H„:μ > 55 b) H₂=55 Ha: #55
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- In a hypothesis test with hypotheses Ho: μ ≤ 54 and H1: μ > 54, a random sample of 24 elements selected from the population produced a mean of 58.6 and a standard deviation of 13.4. The test is to be made at the 10% significance level. Assume the population is normally distributed. What is the critical value of t ?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….A sample of 9 measurements, randomly selected from a normally distributed population, resulted in x= 2.6, and s= 0.9 Conduct a hypothesis test to verify the claim that the population mean is greater than 2.5 . Use a=.05
- 23. The State of California claims the population average of the amount of ice cream each Californian eats in the month of September is 6.85 pints with population standard deviation of 1.35 pints. An SRS of 500 Californians resulted in a sample average of 6.75 pints eaten per person in the month of September At alpha = 0.05 , is there evidence to support the State of California's claim that Californians eat an average of 6.85 pints of ice cream in the month of September? Find the p-value ?A sample of 12 radon detectors of a certain type was selected, and each was exposed to 100 pCi/L of radon. The resulting readings were as follows: 105.6 90.9 91.2 96.9 96.5 91.3 100.1 105.5 99.6 107.7 103.3 92.4 Does this data suggest that the population mean reading under these conditions differ from 100? State the null and alternative hypotheses. Calculate, correct to 2 decimal places, the sample mean, x ; and the sample standard deviation, s. Evaluate the appropriate test statistic. Test these hypotheses at 05 level of significance.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 =
- Suppose that a group of researchers is planning to test a new weight loss supplement. They have selected a random sample of 45 people who are trying to lose weight and plan to measure the amount of weight lost after one month of using the supplement. Assume that the researchers know from prior experiments that the standard deviation of weight lost in one month, , is 1.7 lb. To show that the supplement is effective, they plan to use a one-sample z‑test of Ho : u= 0lb against H1 : u > 0lb , where is the mean amount of weight lost in one month. They have also determined that, for a test with a significance level of 0.05, the power of the test is 0.9347 if the mean amount of weight lost is actually 0.8 lb. What is the probability that the researchers will reject their null hypothesis if the mean amount of weight lost is 0.8 lb or more? Give your answer as a percentage, precise to two decimal places.Recently, the annual number of driver deaths per 100,000 for the selected age groups was as follows: Age Number of Driver Deaths per 100,000 16–19 38 20–24 36 25–34 24 35–54 20 55–74 18 75+ 28 Use the 4 steps of hypothesis testing to see if the prediction is significant with a criteria of alpha=.05 on the following data For each age group, pick the midpoint of the interval for the X value. (For the 75+ group, use 80.)25. The State of California claims the population average of the amount of ice cream each Californian eats in the month of September is 6.85 pints with population standard deviation of 1.35 pints. An SRS of 500 Californians resulted in a sample average of 6.75 pints eaten per person in the month of September . At alpha=0.05, is there evidence to support the State of California's claim that Californians eat an average of 6.85 pints of ice cream in the month of September? Write a conclusion using the context of the problem.
- 24. The State of California claims the population average of the amount of ice cream each Californian eats in the month of September is 6.85 pints with population standard deviation of 1.35 pints. An SRS of 500 Californians resulted in a sample average of 6.75 pints eaten per person in the month of September. At alpha = 0.05 , is there evidence to support the State of California's claim that Californíans eat an average of 6.85 pints of ice cream in the month of September? True or False : Since the p-value is greater than alpha we fail to reject the null hypothesis. True FalseAn electrical engineer wishes to determine if, among two specific municipal buildings in town, Building “North” and Building “South”, whether the tensile strength of pipes (in psi) is not the same in each of these two buildings. A sample of pipes was chosen at random from both Building “North” and Building “South”, respectively. Using α = 0.05, which of the following statistical test, or parameter, would be best for determining whether tensile strength of pipes (in psi) is not the same in each of these two buildings? (Assume all statistical assumptions met.) a) Binomial Distribution b) Population Difference in Means (i.e., Unpaired Data) c) The Chi-Squared Test of Independence d) Population Mean Difference (i.e., Paired Data)A sample of n = 25 subjects has a mean of M = 38.99 and a sample standard deviation of sx = 4.3. In a directional test of H0: μ≤37.27 versus H1: μ>37.27 with α=0.05, this sample produces a tstatistic of t=+2.00. Based on this information, the correct statistical decision is to: