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 μ=20μ=20 inches. However, a survey reported that of a simple random sample of 37 fish caught, the mean length was 17.5 inches, with estimated standard deviation of 4.3 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than μ=20 inches? Use α=0.05. What is the level of significance? State the null and alternate hypotheses. H0:H0:? μ σ χ p Select an answer > = ≠ < H1:H1:? μ χ p σ Select an answer > < = ≠ What sampling distribution will you use? Explain the rationale for you choice of sampling distribution. A) The standard normal, since we have a simple random sample that is large and σσ is known. B) The standard normal, since we have a simple random sample that is large. C) The Student's t, since we have a simple random sample that is large and σσ is known. D) The Student's t, since we have a simple random sample that is large.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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 μ=20μ=20 inches. However, a survey reported that of a simple random sample of 37 fish caught, the
What is the level of significance?
State the null and alternate hypotheses.
H0:H0:? μ σ χ p Select an answer > = ≠ <
H1:H1:? μ χ p σ Select an answer > < = ≠
What sampling distribution will you use? Explain the rationale for you choice of sampling distribution.
- A) The standard normal, since we have a simple random sample that is large and σσ is known.
- B) The standard normal, since we have a simple random sample that is large.
- C) The Student's t, since we have a simple random sample that is large and σσ is known.
- D) The Student's t, since we have a simple random sample that is large.
Given
average length of trout caught in Pyramid Lake is μ = 20 inches.
Sample size = 37
sample mean = x-bar = 17.5 inches
sample standard deviation = 4.3 inches
Null Hypothesis: H0 : μ = 20 inches
Alternative Hypothesis Ha : μ < 20 inches
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