The data table contains waiting times of customers at a bank, where customers enter a single waiting line that feeds three teller windows. Test the claim that the standard deviation of waiting times is less than 2.12.1 minutes, which is the standard deviation of waiting times at the same bank when separate waiting lines are used at each teller window. Use a significance level of 0.050.05. Complete parts (a) through (d) below. LOADING... Click on the icon to view the data. 7.9 6.4 7.3 6.7 7.3 6.4 6.9 7.1 8.3 6.2 6.3 7.2 8.8 6.1 8.9 7.5 7.5 7.6 6.1 7.6 7.3 7.7 7.9 10.1 7.1 6.1 6.5 6.6 6.7 6.9 6.6 6.8 6.9 14.6 6.6 7.2 7.7 7.5 7.6 6.3 13.9 7.2 8.7 7.5 6.1 6.3 7.4 6.1 6.7 6.3 9.1 8.3 6.4 7.9 7.5 8.5 7.8 6.3 6.5 6.5 a. Identify the null and alternative hypotheses. Choose the correct answer below. A. Upper H 0 : sigma greater than or equals 2.1H0: σ≥2.1 minutes Upper H Subscript Upper A Baseline : sigma less than 2.1HA: σ<2.1 minutes B. Upper H 0 : sigma equals 2.1H0: σ=2.1 minutes Upper H Subscript Upper A Baseline : sigma not equals 2.1HA: σ≠2.1 minutes C. Upper H 0 : sigma equals 2.1H0: σ=2.1 minutes Upper H Subscript Upper A Baseline : sigma less than 2.1HA: σ<2.1 minutes Your answer is correct. D. Upper H 0 : sigma less than 2.1H0: σ<2.1 minutes Upper H Subscript Upper A Baseline : sigma equals 2.1HA: σ=2.1 minutes c. Find the P-value of the test statistic. The P-value of the test statistic is:??????? (Round to three decimal places as needed.)
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!
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