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 = 18.6 inches, with estimated standard deviation s = 3.1 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) What is the level of significance? State the null and alternate hypotheses. O Ho: H = 19 in; H,: µ > 19 in O Ho: H< 19 in; H,: µ = 19 in O Ho: H = 19 in; H¸: µ < 19 in O Ho: H = 19 in; H,: µ # 19 in O Ho: H > 19 in; H,: µ = 19 in (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since the sample size is large and o is known. O The standard normal, since the sample size is large and o is known. O The Student's t, since the sample size is large and o is unknown. O 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 pu = 19 inches. However, a survey reported that of a random sample of 46 fish caught, the mean length was x = 18.6 inches, with
estimated standard deviation s = 3.1 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than p = 19 inches? Use
a = 0.05.
(a) What is the level of significance?
State the null and alternate hypotheses.
O Ho: H = 19 in; H,: u > 19 in
O Ho: H < 19 in; H,: µ = 19 in
O Ho: H = 19 in; H,: µ < 19 in
O Ho: H = 19 in; H,: µ # 19 in
O Ho: H > 19 in; H,: µ = 19 in
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
O The Student's t, since the sample size is large and o is known.
The standard normal, since the sample size is large and o is known.
O The Student's t, since the sample size is large and o is unknown.
O 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 pu = 19 inches. However, a survey reported that of a random sample of 46 fish caught, the mean length was x = 18.6 inches, with estimated standard deviation s = 3.1 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than p = 19 inches? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: H = 19 in; H,: u > 19 in O Ho: H < 19 in; H,: µ = 19 in O Ho: H = 19 in; H,: µ < 19 in O Ho: H = 19 in; H,: µ # 19 in O Ho: H > 19 in; H,: µ = 19 in (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since the sample size is large and o is known. The standard normal, since the sample size is large and o is known. O The Student's t, since the sample size is large and o is unknown. O 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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