G. Cannot be determined (c) In part (b), we learned that two groups (students who receive grants and students who do not receive grants) are being ocompared. In addilion, the sampling method is independent. State the null and altemative hypotheses for this test.

Using the dotplot and the proportion of winners in the store owner's sample, is there convincing evidence that the manufacturer's claim is wrong? A manufacturer of bottled tea runs a promotion in which consumers can win a free bottle of tea if the cap of the bottle says "Winner." The manufacturer claims that 1 in 5 bottles is a winner. A store owner Yes, because a proportion of 0.4 or more occurred 25 out of 100 times, the sample proportion of notices that several of the first bottles of tea sold were winners. Suspecting the manufacturer's claim is false, the store owner decides to randomly select 10 bottles of tea from the next shipment from the manufacturer. She is again surprised when 4 of the bottles are winners is statistically significant and there is convincing evidence that the manufacturer's claim is false. Yes, because a proportion of 0.4 or less occurred 75 out of 100 times, the sample proportion of winners. Assuming the manufacturer's claim is true, she simulates 100 values…

a) Which of the following correctly specifies the null hypothesis? [select all that apply] b) Which of the following correctly specifies the alternative hypothesis? [select all that apply] c) Calculate and report the standard error for the sampling distribution for the difference in means.

You work for a marketing firm that has a large client in the automobile industry. You have been asked to estimate the proportion of households in Chicago that have two or more vehicles.  You have been assigned to gather a random sample that could be used to estimate this proportion to within a 0.035 margin of error at a 99% level of confidence. a)  With no prior research, what sample size should you gather in order to obtain a 0.035 margin of error? b)  Your firm has decided that your plan is too expensive, and they wish to reduce the sample size required. You conduct a small preliminary sample, and you obtain a sample proportion of ˆp=0.185. Using this new information. what sample size should you gather in order to obtain a 0.035 margin of error