Pyramid 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 u = 19 inches. However, a survey reported that cof a random sample of 46 fish caught, the mean length was x = 18.4 inches, with estimated standard deviation s = 3.3 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than u = 19 inches? Use a = 0.05. A USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O H,; u > 19 in; H,:# = 19 in O H,i u = 19 in; H,i u # 19 in O H,i u < 19 in; H, u = 19 in O H,i = 19 in; H, 1 u > 19 in O H,i u 19 in; H, u < 19 in (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since the sample size is large and e is known. The Student's r, since the sample size is large and e is known. • The Student's t, since the sample size is large and a is unknown. The standard normal, since the sample size is large and o is unknown. What is the value of the sample test statistic? (Round your answer to three decimal places.)

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Pyramid 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 u = 19 inches. However, a survey reported that of a random sample of 46 fish caught, the mean length
was x = 18.4 inches, with estimated standard deviation s = 3.3 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than u = 19 inches? Use a = 0.05.
A USE SALT
(a) What is the level of significance?
State the null and alternate hypotheses.
O H,1 u > 19 in; H,: u = 19 in
O Hi u = 19 in; H,: u + 19 in
O H; u < 19 in; H,: u = 19 in
O H,i u = 19 in; H,:u > 19 in
O H,i u = 19 in; H,: u < 19 in
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
The standard normal, since the sample size is large and o is known.
The Student's t, since the sample size is large and o is known.
2 The Student's t, since the sample size is large and o is unknown.
The standard normal, since the sample size is large and o is unknown.
What is the value of the sample test statistic? (Round your answer to three decimal places.)
Transcribed Image Text:Pyramid 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 u = 19 inches. However, a survey reported that of a random sample of 46 fish caught, the mean length was x = 18.4 inches, with estimated standard deviation s = 3.3 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than u = 19 inches? Use a = 0.05. A USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O H,1 u > 19 in; H,: u = 19 in O Hi u = 19 in; H,: u + 19 in O H; u < 19 in; H,: u = 19 in O H,i u = 19 in; H,:u > 19 in O H,i u = 19 in; H,: u < 19 in (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since the sample size is large and o is known. The Student's t, since the sample size is large and o is known. 2 The Student's t, since the sample size is large and o is unknown. The standard normal, since the sample size is large and o is unknown. What is the value of the sample test statistic? (Round your answer to three decimal places.)
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