Question

Women are recommended to consume 1730 calories per day. You suspect that the average calorie intake is different for women at your college. The data for the 12 women who participated in the study is shown below:

1844, 1582, 1537, 1594, 1909, 1751, 1900, 1859, 1539, 1604, 1841, 1680

Assuming that the distribution is normal, what can be concluded at the αα = 0.01 level of significance?

1. For this study, we should use Select an answer t-test for a population mean z-test for a population proportion
2. The null and alternative hypotheses would be:

H0:

H1:

3. The test statistic ? z t  =  (please show your answer to 2 decimal places.)
4. The p-value =  (Please show your answer to 4 decimal places.)
5. The p-value is ?
6. Based on this, we should Select an answer reject fail to reject accept  the null hypothesis.
7. 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 1730 at αα = 0.01, so there is insufficient evidence to conclude that the population mean calorie intake for women at your college is different from 1730.
   • The data suggest the population mean is not significantly different from 1730 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 1730.
   • The data suggest the populaton mean is significantly different from 1730 at αα = 0.01, so there is sufficient evidence to conclude that the population mean calorie intake for women at your college is different from 1730.
8. Interpret the p-value in the context of the study.
   • If the population mean calorie intake for women at your college is 1730 and if you survey another 12 women at your college then there would be a 81.68755208% chance that the population mean would either be less than 1740 or greater than 1720.
   • There is a 81.68755208% chance of a Type I error.
   • If the population mean calorie intake for women at your college is 1730 and if you survey another 12 women at your college, then there would be a 81.68755208% chance that the sample mean for these 12 women would either be less than 1740 or greater than 1720.
   • There is a 81.68755208% chance that the population mean calorie intake for women at your college is not equal to 1730.
9. Interpret the level of significance in the context of the study.
   • If the population mean calorie intake for women at your college is different from 1730 and if you survey another 12 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 1730.
   • There is a 1% chance that the population mean calorie intake for women at your college is different from 1730.
   • 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 1730 and if you survey another 12 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 1730.

Answer 1

1 ) For this study, we should use t-test for a population mean because of sigma is known

2 )The null and alternative hypotheses would be:

H0: u= 1730

H1:u 1730

using excel we have

t Test for Hypothesis of the Mean
Data
Null Hypothesis                m=	1730
Level of Significance	0.01
Sample Size	12
Sample Mean	1720
Sample Standard Deviation	146.0529169
Intermediate Calculations
Standard Error of the Mean	42.1618
Degrees of Freedom	11
t Test Statistic	-0.2372
Two-Tail Test
Lower Critical Value	-3.1058
Upper Critical Value	3.1058
p-Value	0.8169
Do not reject the null hypothesis

1. The test statistic t  = -0.24
2. The p-value = 0.8169
3. Based on this, we should accept  the null hypothesis.
4. Thus, the final conclusion is that ...
   • The data suggest the population mean is not significantly different from 1730 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 1730.
5. Interpret the p-value in the context of the study.
   • There is a 81.68755208% chance of a Type I error.
6. Interpret the level of significance in the context of the study.
   • If the population mean calorie intake for women at your college is different from 1730 and if you survey another 12 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 1730.