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- a cereal company claims that the mean weight of the cereal in its packets is at least 14oz. express the null hypothesis and the alternatvie hypothesis in symbolic formLet X1 and X2 constitute a random sample from a nor-mal population with σ2 = 1. If the null hypothesis μ = μ0 is to be rejected in favor of the alternative hypothesis μ = μ1 > μ0 when x > μ0 + 1, what is the size of the criti-cal region?The fire department of a city wants to test the null hypothesis that σ =10 minutes for the time it takes a fire truck to reach a fire site against thealternative hypothesis σ 6= 10 minutes. What can it conclude at the 0.05 levelof significance if a random sample of size n = 48 yields s = 9.5minutes?
- If X1, X2, ... , Xn constitute a random sample from anormal population with μ = 0, show that ni=1X2inis an unbiased estimator of σ2.A geneticist working on peas has a single plant monohybrid Y/y (yellow) plant and, from a self of this plant,wants to produce a plant of genotype y/y to use as a tester. How many progeny plants need to be grown to be 95percent sure of obtaining at least one in the sample?An organization published an article stating that in any one-year period, approximately 11.5 percent of adults in a country suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, nine of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult population in the country. At a pre-conceived α = 0.05, what are your following?Decision: , Reason for the decision: ,Conclusion
- You may use homogenous, exact/inexact, linear, Bernoulli, or second order reducible to first orderA commonly cited study says that 49% of students study less than 5 hours per week. A researcher does not think this is accurate and wants to show that the percentage of students that study less than 5 hours per week is not equal to 49%. Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter p.A researcher is using a two-tailed hypothesis test with α = 0.01 to evaluate the effect of a treatment. If theboundaries for the critical region are t = ± 2.845, then how many individuals are in the sample
- A particular orchid species has extensions on its flowers called nectar spurs. It has been hypothesized that these spurs improve pollination by requiring long-tongued pollinators to press further against the flower in order to reach the distant nectar at the bottom of the spur. To test this, researchers shortened the spurs of 59 orchids, while leaving another 59 orchids intact as controls. After a week, they found that 10 of the shortened flowers had been pollinated, while 27 of the control flowers had been pollinated. How would you test whether there was a difference in pollination rate for shortened vs. intact flowers?A card company claims that 80% of all American college students send a card to their mother on Mother's Day. You take a random sample of 125 American college students and find that 70% of them sent a card to their mother on Mother's Day. At a .05 alpha level, can you prove or disprove the card company's claim? Show all work.A random group of apartments was selected from a city to analyze the number of bedrooms they have. there evidence to reject the hypothesis that the apartments are equally distributed between 1-bedroom, 2 bedroom and 3-bedroom apartments , at alpha = 0.05