Question

On average, Americans have lived in 2 places by the time they are 18 years old. Is this average more for college students? The 57 randomly selected college students who answered the survey question had lived in an average of 2.17 places by the time they were 18 years old. The standard deviation for the survey group was 0.8. What can be concluded at the αα = 0.10 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:  ? p μ  ? = ≠ < > _________

H1:  ? p μ  ? < = ≠ > _________   

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 ? ≤ >  α
6. Based on this, we should Select an answer fail to reject reject accept  the null hypothesis.g
7. Thus, the final conclusion is that ...
   • The data suggest that the populaton mean is significantly more than 2 at αα = 0.10, so there is statistically significant evidence to conclude that the population mean number of places that college students lived in by the time they were 18 years old is more than 2.
   • The data suggest that the population mean is not significantly more than 2 at αα = 0.10, so there is statistically insignificant evidence to conclude that the population mean number of places that college students lived in by the time they were 18 years old is more than 2.
   • The data suggest that the sample mean is not significantly more than 2 at αα = 0.10, so there is statistically insignificant evidence to conclude that the sample mean number of places that college students lived in by the time they were 18 years old is more than 2.17.
8. Interpret the p-value in the context of the study.
   • If the population mean number of places that college students lived in by the time they were 18 years old is 2 and if you survey another 57 college students then there would be a 5.71323686% chance that the population mean number of places that these college students lived in by the time they were 18 years old would be greater than 2.
   • If the population mean number of places that college students lived in by the time they were 18 years old is 2 and if you survey another 57 college students then there would be a 5.71323686% chance that the sample mean for these 57 college students would be greater than 2.17.
   • There is a 5.71323686% chance of a Type I error.
   • There is a 5.71323686% chance that the population mean number of places that college students lived in by the time they were 18 years old is greater than 2 .
9. Interpret the level of significance in the context of the study.
   • If the population mean number of places that college students lived in by the time they were 18 years old is more than 2 and if you survey another 57 college students, then there would be a 10% chance that we would end up falsely concuding that the population mean number of places that college students lived in by the time they were 18 years old is equal to 2.
   • If the population mean number of places that college students lived in by the time they were 18 years old is 2 and if you survey another 57 college students, then there would be a 10% chance that we would end up falsely concuding that the population mean number of places that college students lived in by the time they were 18 years old is more than 2.
   • There is a 10% chance that the population mean number of places that college students lived in by the time they were 18 years old is more than 2.
   • There is a 10% chance that none of this is real since you have been hooked up to virtual reality since you were born.

Answer 1

Solution:-

a) We should use t-test for a population mean.

b)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u = 2.0
Alternative hypothesis: u > 2.0

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.10. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 0.10596
DF = n - 1

D.F = 56
a)

t = (x - u) / SE

t = 1.60

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a t statistic test statistic of 1.60.

b) P-value = P(t > 1.60)

Use t-value calculator to find p-value

P-value = 0.058

c) Interpret results. Since the P-value (0.058) is less than the significance level (0.10), we have to reject the null hypothesis.

d) Based on this, we should fail to reject reject null hypothesis.

e)

Thus, the final conclusion is that The data suggest that the populaton mean is significantly more than 2 at αα = 0.10, so there is statistically significant evidence to conclude that the population mean number of places that college students lived in by the time they were 18 years old is more than 2.

f) If the population mean number of places that college students lived in by the time they were 18 years old is 2 and if you survey another 57 college students then there would be a 5.71323686% chance that the sample mean for these 57 college students would be greater than 2.17.

g)

If the population mean number of places that college students lived in by the time they were 18 years old is 2 and if you survey another 57 college students, then there would be a 10% chance that we would end up falsely concuding that the population mean number of places that college students lived in by the time they were 18 years old is more than 2.