A random sample of 51 measurements produced the following sums: Σχ=50.3 Ex=68 a. Test the null hypothesis that u=1.18 against the alternative that b. Test the null hypothesis that u=1.18 against the alternative that <1.18. Use a = .01. <1.18. Use a = .10.
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- Travis does research with a marine biology research team. His job is to catch lobsters, weigh them, tag them, and return them to the water. Over the years, the team has determined that the average weight in pounds of the lobsters caught at a particular location was µ = 2.1 lbs. with a σ of 1.8 lbs. As part of an annual survey, Travis catches 27 lobsters with a mean of 3.1 lbs. Is he correct in assuming that the lobsters he caught are significantly heavier that those usually found in that location? Please use α = .05 and a two-tailed test.a. Compute the p-value for the test (use R). Round to the nearest 3rd decimal place, 0.xxx. b. Make and justify a statistical decision at the α= 0.05 significance level and state your conclu-sions in context of the problem.a. Compute the p-value for the test (use R). Round to the nearest 3rd decimal place, 0.xxx. b. Make and justify a statistical decision at the α= 0.15 significance level and state your conclu-sions in context of the problem.
- A sample of sizen = 100 is used to test H,: µ 20. The value of u will not have practical significance unless µ > 25. The population standard deviation is o = 10. The value of xis 21. Assume the sample size is n = 100. Compute the P-value. Show that you do not reject Но- Assume the sample size is n = 1000. Compute the P-value. Show that you reject Họ. Do you think the difference is likely to be of practical significance? Explain. d. Explain why a larger sample can be more likely to produce a statistically significant result that is not of practical significance. a. b. C.A sample of n sludge specimens is selected and the pH of each one is determined. The one-sample t test will then be used to see if there is compelling evidence for concluding that true average pH is less than 7.0. What conclusion is appropriate in each of the following situations? USE SALT (a) n = 8, t= -2.8, a = 0.05 O Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0. O Reject the null hypothesis. There is not sufficient evidence that the true average pH is less than 7.0. O Do not reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0. O Do not reject the null hypothesis. There is not sufficient evidence that the true average pH is less than 7.0. (b) n = 15, t= -3.5, a = 0.01 O Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0. O Reject the null hypothesis. There is not sufficient evidence that the true average pH is less than 7.0. O Do not…Determine the rejection region for a hypothesis test for the population mean using the give information. Assume that the population standard deviation is unknown, the sample size is small, and the population distribution is approximately normal. Write your answer in a format exactly as in the following examples, "t <= -2.203", or "t >= 1.706", or "|t| >= 1.305". Do not forget the SPACE after t and the SPACE before the number. Also make sure to enter the digit 0 before the decimal point. ?=0.90,??=18 two-tailed test Reject H0 if
- Laura asks whether the type of school students attend (private versus public) results in different performance on a test. A sample of N=100 students from a private school produce a mean of 71.30 on a test, and the mean of the population of public school students is µ=75.62 with ?௫ =28. a. Write the alternative hypothesis. b. Write the null hypothesis. c. With α=.05, what is zcrit? d. Compute zobt e. What should Laura conclude?Let X-1: correct, X=0 : wrong And P= Pr(X=1)=2/5 What is the variance? .32 O.6 O .4The NAEP considers that a national average of 283 is an acceptable performance. Using α = .05, run a two-tail t-test for one sample to test Ho: µ=283 for the 2019 scores. Report the t-obt, df, and p-values. Would you reject the null hypothesis that the 2019 scores come from a population with average 283? If this is the case, does it come from a population from larger or smaller average?
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