In: Math
Women are recommended to consume 1900 calories per day. You suspect that the average calorie intake is smaller for women at your college. The data for the 15 women who participated in the study is shown below: 1625, 1927, 1996, 1762, 1766, 1885, 2008, 1751, 1666, 1837, 1981, 1603, 1881, 1606, 1625 Assuming that the distribution is normal, what can be concluded at the α α = 0.05 level of significance? a.For this study, we should use Select an answer z-test for a population proportion t-test for a population mean b.The null and alternative hypotheses would be: H0: H0: ? μ p ? = > < ≠ H1: H1: ? μ p ? < > = ≠ c.The test statistic ? z t = (please show your answer to 3 decimal places.) d.The p-value = (Please show your answer to 4 decimal places.) e.The p-value is ? ≤ > α α f.Based on this, we should Select an answer reject accept fail to reject the null hypothesis. g.Thus, the final conclusion is that ... The data suggest the populaton mean is significantly less than 1900 at α α = 0.05, so there is sufficient evidence to conclude that the population mean calorie intake for women at your college is less than 1900. The data suggest the population mean is not significantly less than 1900 at α α = 0.05, so there is sufficient evidence to conclude that the population mean calorie intake for women at your college is equal to 1900. The data suggest that the population mean calorie intake for women at your college is not significantly less than 1900 at α α = 0.05, so there is insufficient evidence to conclude that the population mean calorie intake for women at your college is less than 1900. h.Interpret the p-value in the context of the study. If the population mean calorie intake for women at your college is 1900 and if you survey another 15 women at your college, then there would be a 0.7648994% chance that the sample mean for these 15 women would be less than 1795. If the population mean calorie intake for women at your college is 1900 and if you survey another 15 women at your college, then there would be a 0.7648994% chance that the population mean calorie intake for women at your college would be less than 1900. There is a 0.7648994% chance that the population mean calorie intake for women at your college is less than 1900. There is a 0.7648994% chance of a Type I error. i.Interpret the level of significance in the context of the study. If the population mean calorie intake for women at your college is less than 1900 and if you survey another 15 women at your college, then there would be a 5% chance that we would end up falsely concuding that the population mean calorie intake for women at your college is equal to 1900. There is a 5% chance that the population mean calorie intake for women at your college is less than 1900. If the population mean calorie intake for women at your college is 1900 and if you survey another 15 women at your college, then there would be a 5% chance that we would end up falsely concuding that the population mean calorie intake for women at your college is less than 1900. There is a 5% chance that the women at your college are just eating too many desserts and will all gain the freshmen 15.
e) The p-value is ≤ α
f) Based on this, we should reject the null hypothesis.
g) Thus, the final conclusion is that -
The data suggest the population mean is significantly less than 1900 at α α = 0.05, so there is sufficient evidence to conclude that the population mean calorie intake for women at your college is less than 1900.
h) If the population mean calorie intake for women at your college is 1900 and if you survey another 15 women at your college, then there would be a 0.7648994% chance that the sample mean for these 15 women would be less than 1795.
i) If the population mean calorie intake for women at your college is 1900 and if you survey another 15 women at your college, then there would be a 5% chance that we would end up falsely concuding that the population mean calorie intake for women at your college is less than 1900.