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 ? = 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 = 3.1 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than ? = 19 inches? Use ? = 0.05. a) State the null and alternate hypotheses. select one: H0: ? = 19 in; H1: ? > 19 in H0: ? = 19 in; H1: ? < 19 in H0: ? < 19 in; H1: ? = 19 in H0: ? = 19 in; H1: ? ≠ 19 in H0: ? > 19 in; H1: ? = 19 in 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 ? is unknown. The standard normal, since the sample size is large and ? is known. The Student's t, since the sample size is large and ? is known. The standard normal, since the sample size is large and ? is unknown. c) What is the value of the sample test statistic? (Round your answer to three decimal places.)
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 ? = 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 = 3.1 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than ? = 19 inches? Use ? = 0.05.
a) State the null and alternate hypotheses. select one:
H0: ? = 19 in; H1: ? > 19 in
H0: ? = 19 in; H1: ? < 19 in
H0: ? < 19 in; H1: ? = 19 in
H0: ? = 19 in; H1: ? ≠ 19 in
H0: ? > 19 in; H1: ? = 19 in
b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
The Student's t, since the
The standard normal, since the sample size is large and ? is known.
The Student's t, since the sample size is large and ? is known.
The standard normal, since the sample size is large and ? is unknown.
c) What is the value of the sample test statistic? (Round your answer to three decimal places.)
Given:
Population mean
Sample size
Sample mean
Sample standard deviation
Level of significance
The test statistic is,
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