The mean potassium content of a popular sports drink is listed as 140 mg in a 32-ounce bottle. Analysis of 20 bottles of the drink indicates a sample mean of 139.40 mg. The population standard deviation is known to be 2.00mg. At 10 percent level of significance (α = .10), does the sample contradict the manufacturer’s claim? Use the format of questions below, (i) to (vi) to answer this question. (i) State the null and alternative hypotheses. (ii) Compute the appropriate test statistic. (iii) Determine the p-value.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The mean potassium content of a popular sports drink is listed as 140 mg in a 32-ounce bottle. Analysis of 20 bottles of the drink indicates a sample mean of 139.40 mg. The population standard deviation is known to be 2.00mg. At 10 percent level of significance (α = .10), does the sample contradict the manufacturer’s claim? Use the format of questions below, (i) to (vi) to answer this question.
(i) State the null and alternative hypotheses.
(ii) Compute the appropriate test statistic.
(iii) Determine the p-value.
(iv) What is the critical value?
(v) What is the statistical decision? (That is, reject H0 or fail to reject H0). Also state the criterion your decision is based on.
(vi) What is your conclusion?
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