A hypothesis test is performed to determine if the proportion of all six packs of seltzers sold in a particular grocery store near a college campus that are alcoholic exceeds 50%. A random sample of 152 customers that purchased seltzer is acquired (assume no customer purchases more than one six pack at time, alcoholic or not); the sample proportion of these purchases that are alcoholic is obtained. From this sample a test statistic of 2.60 is calculated, which has a corresponding P-value of 0.0047. Which of the following is true? Select one: Oa. The probability that, in a random sample of 152 customers purchasing seltzers, more than 50% of those customers will have purchased alcoholic seltzer is 0.0047. b. None of these statements is true. c. The probability the null hypothesis is true is $1 - 0.0047 = 0.9953$. Od. The probability that 50% of customers purchasing seltzers will be purchasing alcoholic seltzer on any given day is 0.0047. Oe. The probability the null hypothesis is true is 0.0047. Which of the following are true of P-values? Select one or more: a. Together with the significance level $alpha$, they determine whether or not we reject the $H_0$. b. They are between 0 and 1. c. Their calculation in a hypothesis test depends on the alternative hypothesis $H_A$. d. They are calculated assuming the null hypothesis $H_0$ is true in a hypothesis test. e. They represent the probability the null hypothesis $H_0$ is true in a hypothesis test. f. They are used to determine the margin of error of confidence intervals
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The probability that, in a random sample of 152 customers purchasing seltzers, more than 50% of those customers will have purchased alcoholic seltzer is 0.0047. This statement is incorrect. The P-value represents the probability of observing a test statistic as Show more…
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A hypothesis test is performed to determine if the proportion of all six packs of seltzers sold in a particular grocery store near a college campus that are alcoholic exceeds 50%. A random sample of 152 customers that purchased seltzer is acquired (assume no customer purchases more than one six pack at a time, alcoholic or not); the sample proportion of these purchases that are alcoholic is obtained. From this sample, a test statistic of 2.60 is calculated, which has a corresponding P-value of 0.0047. Which of the following is true? Select one: a. The probability the null hypothesis is true is 0.0047. b. The probability that in a random sample of 152 customers purchasing seltzers, more than 50% of those customers will have purchased alcoholic seltzer is 0.0047. c. None of these statements is true. d. The probability that 50% of customers purchasing seltzers will be purchasing alcoholic seltzer on any given day is 0.0047. e. The probability the null hypothesis is true is 1-0.0047 = 0.9953.
Adi S.
In assessing the validity of any test of hypotheses, it is good practice to answer the following question: a) test the hypotheses at several different levels of significance b) examine the probability model by using exploratory data analysis on the data c) test both one- and two-sided hypotheses to help guarantee consistency d) All of the above
Sri K.
According to a study done in 2013, the average age of a first-time home buyer in Canada was 29.6 years old. A researcher believes this number has increased since that time. A large random sample of Canadian first-time homebuyers is selected to test this claim. a. Determine what population parameter is being tested: μ: population mean b. Determine if the alternative hypothesis is a left-tailed, right-tailed, or two-tailed test: < : left-tailed > : right-tailed ≠ : two-tailed 2. H0: μ = 18 kg H1: μ > 18 kg Level of significance: α = 0.025 Sample size: n = 36 Test statistic: t = 2.305 Unknown population standard deviation T-Distribution Table a. Determine the critical value(s) for the proposed hypothesis test. ± Round to three decimal places if necessary b. Conclude whether to reject the null hypothesis or not based on the test statistic. Reject Fail to Reject c. State the decision error type that is possible. Type I Error Type II Error 3. The restaurant manager is testing the bartender's ability to pour 45 mL of spirits correctly into a mixed drink. The manager has the bartender pour water into 12 shot glasses to test their ability to pour the correct amount of spirits: 48 45 44 43 46 47 42 46 47 45 47 49 Note: The data appears to be approximately normally distributed. Test the bartender's ability to pour 45 mL at the 5% level of significance. T-Distribution Table a. Calculate the sample mean and standard deviation. x̄ = Round to three decimal places if necessary s = Round to three decimal places if necessary b. Calculate the test statistic. t = Round to three decimal places if necessary c. Determine the critical value(s) for the hypothesis test. ± Round to three decimal places if necessary d. Conclude whether to reject the null hypothesis or not based on the test statistic. Reject Fail to Reject
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