Question

Women are recommended to consume 1830 calories per day. You suspect that the average calorie intake is different for women at your college. The data for the 13 women who participated in the study is shown below: 1940, 1678, 1666, 1757, 1517, 1529, 1702, 1842, 1919, 1738, 1676, 1796, 1924 Assuming that the distribution is normal, what can be concluded at the α α = 0.01 level of significance? For this study, we should use The null and alternative hypotheses would be: H 0 : H 0 : H 1 : H 1 : The test statistic = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is α α Based on this, we should 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 different from 1830 at α α = 0.01, so there is insufficient evidence to conclude that the population mean calorie intake for women at your college is different from 1830. The data suggest the populaton mean is significantly different from 1830 at α α = 0.01, so there is sufficient evidence to conclude that the population mean calorie intake for women at your college is different from 1830. The data suggest the population mean is not significantly different from 1830 at α α = 0.01, so there is sufficient evidence to conclude that the population mean calorie intake for women at your college is equal to 1830. Interpret the p-value in the context of the study. There is a 4.62023622% chance of a Type I error. If the population mean calorie intake for women at your college is 1830 and if you survey another 13 women at your college, then there would be a 4.62023622% chance that the sample mean for these 13 women would either be less than 1915 or greater than 1745. There is a 4.62023622% chance that the population mean calorie intake for women at your college is not equal to 1830. If the population mean calorie intake for women at your college is 1830 and if you survey another 13 women at your college then there would be a 4.62023622% chance that the population mean would either be less than 1915 or greater than 1745. Interpret the level of significance in the context of the study. There is a 1% chance that the women at your college are just eating too many desserts and will all gain the freshmen 15. If the population mean calorie intake for women at your college is 1830 and if you survey another 13 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 different from 1830. There is a 1% chance that the population mean calorie intake for women at your college is different from 1830. If the population mean calorie intake for women at your college is different from 1830 and if you survey another 13 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 1830.

Answer 1

∑x = 22684

∑x² = 39810360

n = 13

Mean , x̅ = Ʃx/n = 22684/13 = 1744.9231

Standard deviation, s = √[(Ʃx² - (Ʃx)²/n)/(n-1)] = √[(39810360-(22684)²/13)/(13-1)] = 137.9991

Null and Alternative hypothesis:

Ho : µ = 1830

H1 : µ ≠ 1830

Test statistic:

t = (x̅ - µ)/(s/√n) = (1744.9231 - 1830)/(137.9991/√13) = -2.223

df = n-1 = 12

Two tailed p-value = T.DIST.2T(ABS(-2.2228), 12) = 0.0462

The p-value is > α

Based on this, we should fail to 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 different from 1830 at α = 0.01, so there is insufficient evidence to conclude that the population mean calorie intake for women at your college is different from 1830.

Interpret the p-value in the context of the study.

If the population mean calorie intake for women at your college is 1830 and if you survey another 13 women at your college then there would be a 4.62023622% chance that the population mean would either be less than 1915 or greater than 1745.

Interpret the level of significance in the context of the study.

There is a 1% chance that the population mean calorie intake for women at your college is different from 1830.