Question

10.A random sample of 25 values is drawn from a mound-shaped and symmetric distribution. The sample mean is

11 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 10.5.

(a) Is it appropriate to use a Student’s t distribution? Explain.

Yes, because the x distribution is mound-shaped and symmetric and σ is unknown.

No, the x distribution is skewed left.  

No, the x distribution is skewed right.

No, the x distribution is not symmetric.

No, σ is known.

How many degrees of freedom do we use?

(c) Compute the t value of the sample test statistic. (Round your answer to three decimal places.)

t = 

12Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is μ = 19 inches. However, a survey reported that of a random sample of 51 fish caught, the mean length was x = 18.6 inches, with estimated standard deviation s = 2.9 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than μ = 19 inches? Use α = 0.05.

(a) What is the level of significance?

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student’s t, since the sample size is large and σ is known.

The standard normal, since the sample size is large and σ is unknown.  

The Student’s t, since the sample size is large and σ is unknown.

The standard normal, since the sample size is large and σ is known.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

Looking for a Similar Assignment? Order now and Get 10% Discount! Use Coupon Code "Newclient"