The average wait time to get seated at a popular restaurant in the city on a Friday night is 14 minutes. Is the mean wait time greater for men who wear a tie? Wait times for 14 randomly selected men who were wearing a tie are shown below. Assume that the distribution of the population is normal. 15, 15, 15, 12, 13, 13, 15, 15, 14, 15, 16, 14, 16, 16 What can be concluded at the the αα = 0.05 level of significance level of significance? For this study, we should use z or t test? The null and alternative hypotheses would be: H0:H0: H1:H1: The test statistic = ? ( 3 decimal places.) The p-value = ? ( 4 decimal places.) The p-value is greater or less than A? Based on this, we should reject, accept or fail to reject the null hypothesis? Thus, the final conclusion is that ... The data suggest the populaton mean is significantly more than 14 at αα = 0.05, so there is statistically significant evidence to conclude that the population mean wait time for men who wear a tie is more than 14. The data suggest that the population mean wait time for men who wear a tie is not significantly more than 14 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean wait time for men who wear a tie is more than 14. The data suggest the population mean is not significantly more than 14 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean wait time for men who wear a tie is equal to 14.
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 average wait time to get seated at a popular restaurant in the city on a Friday night is 14 minutes. Is the mean wait time greater for men who wear a tie? Wait times for 14 randomly selected men who were wearing a tie are shown below. Assume that the distribution of the population is normal.
15, 15, 15, 12, 13, 13, 15, 15, 14, 15, 16, 14, 16, 16
What can be concluded at the the αα = 0.05 level of significance level of significance?
- For this study, we should use z or t test?
- The null and alternative hypotheses would be:
H0:H0:
H1:H1:
- The test statistic = ? ( 3 decimal places.)
- The p-value = ? ( 4 decimal places.)
- The p-value is greater or less than A?
- Based on this, we should reject, accept or fail to reject the null hypothesis?
- Thus, the final conclusion is that ...
- The data suggest the populaton mean is significantly more than 14 at αα = 0.05, so there is statistically significant evidence to conclude that the population mean wait time for men who wear a tie is more than 14.
- The data suggest that the population mean wait time for men who wear a tie is not significantly more than 14 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean wait time for men who wear a tie is more than 14.
- The data suggest the population mean is not significantly more than 14 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean wait time for men who wear a tie is equal to 14.
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