Question
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
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= 19inches. However, a survey reported that of a random sample of51fish caught, the mean length wasxbar=18.5inches, with estimated standard deviations=3.1inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than= 19inches? Use= 0.05
(a) What is the level of significance?
State the null and alternate hypotheses.
- 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 standard normal, since the sample size is large andis unknown.
- The standard normal, since the sample size is large andis known.
- The Student'st, since the sample size is large andis unknown.
- The Student'st, since the sample size is large andis known.
What is the value of the sample test statistic? (Round your answer to three decimal places.)
(c) Estimate theP-value.
- P-value > 0.250
- 0.100 <P-value < 0.250
- 0.050 <P-value < 0.100
- 0.010 <P-value < 0.050
- P-value < 0.010
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?
- At the= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
- At the= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
- At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
- At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
- There is sufficient evidence at the 0.05 level to conclude that the average fish length is less than 19 inches.
- There is insufficient evidence at the 0.05 level to conclude that the average fish length is less than 19 inches.
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