Women are recommended to consume 1790 calories per day. You suspect that the average calorie intake is larger for women at your college. The data for the 11 women who participated in the study is shown below: 2035, 2079, 1842, 1923, 1701, 1889, 1691, 1731, 1730, 2006, 1954 Assuming that the distribution is normal, what can be concluded at the αα = 0.01 level of significance? For this study, we should use Select an answer t-test for a population mean z-test for a pop
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!
Women are recommended to consume 1790 calories per day. You suspect that the average calorie intake is larger for women at your college. The data for the 11 women who participated in the study is shown below:
2035, 2079, 1842, 1923, 1701, 1889, 1691, 1731, 1730, 2006, 1954
Assuming that the distribution is normal, what can be concluded at the αα = 0.01 level of significance?
- For this study, we should use Select an answer t-test for a population
mean z-test for a population proportion - The null and alternative hypotheses would be:
H0:H0: ? p μ Select an answer = > < ≠
H1:H1: ? μ p Select an answer ≠ < = >
- The test statistic ? t z = (please show your answer to 3 decimal places.)
- The p-value = (Please show your answer to 4 decimal places.)
- The p-value is ? ≤ > αα
- Based on this, we should Select an answer accept fail to reject reject the null hypothesis.
- Thus, the final conclusion is that ...
- The data suggest that the population mean calorie intake for women at your college is not significantly more than 1790 at αα = 0.01, so there is insufficient evidence to conclude that the population mean calorie intake for women at your college is more than 1790.
- The data suggest the populaton mean is significantly more than 1790 at αα = 0.01, so there is sufficient evidence to conclude that the population mean calorie intake for women at your college is more than 1790.
- The data suggest the population mean is not significantly more than 1790 at αα = 0.01, so there is sufficient evidence to conclude that the population mean calorie intake for women at your college is equal to 1790.
- Interpret the p-value in the context of the study.
- If the population mean calorie intake for women at your college is 1790 and if you survey another 11 women at your college then there would be a 4.33126992% chance that the sample mean for these 11 women would be greater than 1871.
- If the population mean calorie intake for women at your college is 1790 and if you survey another 11 women at your college then there would be a 4.33126992% chance that the population mean calorie intake for women at your college would be greater than 1790.
- There is a 4.33126992% chance that the population mean calorie intake for women at your college is greater than 1790.
- There is a 4.33126992% chance of a Type I error.
- Interpret the level of significance in the context of the study.
- If the population mean calorie intake for women at your college is 1790 and if you survey another 11 women at your college, then there would be a 1% chance that we would end up falsely concuding that the population mean calorie intake for women at your college is more than 1790.
- If the population mean calorie intake for women at your college is more than 1790 and if you survey another 11 women at your college, then there would be a 1% chance that we would end up falsely concuding that the population mean calorie intake for women at your college is equal to 1790.
- There is a 1% chance that the population mean calorie intake for women at your college is more than 1790.
- There is a 1% chance that the women at your college are just eating too many desserts and will all gain the freshmen 15.
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