Question

The mean number of eggs per person eaten in the United States is 245. Do college students eat a different number of eggs than the average American? The 53 college students surveyed averaged 265 eggs per person and their standard deviation was 61.5. What can be concluded at the αα = 0.05 level of significance?

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

H0:H0:  ? p μ  ? < = ≠ >       

H1:H1:  ? μ p  ? > < = ≠    

3. The test statistic ? t z  =  (please show your answer to 3 decimal places.)
4. The p-value =  (Please show your answer to 4 decimal places.)
5. The p-value is ? ≤ >  αα
6. Based on this, we should Select an answer reject accept fail to reject  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest that the population mean is not significantly different from 245 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean number of eggs consumed by college students per year is different from 245.
   • The data suggest that the sample mean is not significantly different from 245 at αα = 0.05, so there is statistically insignificant evidence to conclude that the sample mean number of eggs consumed by college students per year is different from 265.
   • The data suggest that the populaton mean is significantly different from 245 at αα = 0.05, so there is statistically significant evidence to conclude that the population mean number of eggs consumed by college students per year is different from 245.
8. Interpret the p-value in the context of the study.
   • If the population mean number of eggs consumed by college students per year is 245 and if another 53 college students are surveyed then there would be a 2.16632416% chance that the population mean would either be less than 225 or greater than 265.
   • There is a 2.16632416% chance of a Type I error.
   • If the population mean number of eggs consumed by college students per year is 245 and if another 53 college students are surveyed then there would be a 2.16632416% chance that the sample mean for these 53 students surveyed would either be less than 225 or greater than 265.
   • There is a 2.16632416% chance that the population mean number of eggs consumed by college students per year is not equal to 245.
9. Interpret the level of significance in the context of the study.
   • If the population mean number of eggs consumed by college students per year is 245 and if another 53 college students are surveyed then there would be a 5% chance that we would end up falsely concluding that the population mean number of eggs consumed by college students per year is different from 245.
   • There is a 5% chance that you will find the chicken that lays the golden eggs.
   • There is a 5% chance that the population mean number of eggs consumed by college students per year is different from 245.
   • If the population population mean number of eggs consumed by college students per year is different from 245 and if another 53 college students are surveyed then there would be a 5% chance that we would end up falsely concluding that the population mean number of eggs consumed by college students per year is equal to 245.

Answer 1