#10 Basic Computation: Testing , Unknown

A random sample has 49 values.The sample mean is 8.5 and the sample standard deviation is 1.5.Use a level of significance of 0.01 to conduct a left-handed test of the claim that the population mean is 9.2.

(a)Is it appropriate to use a Student's t distribution?Explain.How many degrees of freedom do we use?

(b)What are the hypotheses?

(c)Compute the t value of the sample test statistic.

(d)Estimate the P-value for the test.

(e)Do we reject or fail to reject the null hypotheses H₀ ?

(f)Interpret the results.

#14 Fishing: TroutA lake is famous for cutthroat trout.Suppose a friend tells you that the average length of the trout is = 19 inches.However a survey reported that of a random sample of 51 fish caught, the mean length was inches, with estimated standard deviation s = 3.2 inches.Does this data indicate that the average length of a trout in this lake is less than = 19 inches?Use = 0.05.

(a)Is it appropriate to use a Student's t distribution?Explain.How many degrees of freedom do we use?

(b)What are the hypotheses?

(c)Compute the t value of the sample test statistic.

(d)Estimate the P-value for the test.

(e)Do we reject or fail to reject the null hypotheses H₀ ?

(f)Interpret the results.

Section 8.3

#6 Basic Computation: Testing pA random sample of 60 binomial trials resulted in 18 successes.Test the claim that the population proportion of successes exceeds 18%.Use a level of significance of 0.01.

(a)Can a normal distribution be used for the distribution?Explain.

(b)State the hypotheses.

(c)Compute and the corresponding standardized sale test statistic.

(d)Find the P-value of the test statistic.

(e)Do you reject or fail to reject the H₀ ? Explain.

(f)What do the results tell you?

#12 Preference: ColorWhat is your favorite color?A large survey indicates that most people prefer the color Blue.In fact, about 24% of the population claim blue is their favorite color.Suppose a random sample ofn = 56 college students were surveyed and r = 12 of them said that blue is their favorite color.Does this information imply that the color preference of all college students is different (either way) from that of the general population? Use = 0.05.

a.What is the level of significance?State the null and alternate hypotheses.

b.What sampling distribution will you use?Do you think the sample size is sufficiently large?Explain.Compute the value of the sample test statistic and corresponding z value.

c.Find the P-value of the test statistic.Sketch the sampling distribution and show the area corresponding to the P-value.

d.Based on your answers in parts (a), (b), and (c), will you reject or fail to reject the null hypotheses?Are the data statistically significant at level ?

e.Interpret your conclusion in the context of the application.