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 length of trough caught in Pyramid Lake is mu = 19 inches. However, the Creel Survey reported that of a random sample of 51 fish caught, the mean length was x-bar = 18.5 inches, with estimated standard deviation s = 3.2 inches. Do these data indicate that the average length of a trout caught in Pyramid lake is less than mu = 19 inches? Use alpha = 0.05.

Answer 1

To determine if the average length of a trout caught in Pyramid Lake is less than 19 inches, we can conduct a hypothesis test. The data does not provide sufficient evidence to conclude that the average length is less than 19 inches.

Step-by-step explanation:

To determine whether the average length of a trout caught in Pyramid Lake is less than 19 inches, we can conduct a hypothesis test. We set up the null hypothesis, H0, as the average length being equal to 19 inches, and the alternative hypothesis, Ha, as the average length being less than 19 inches. We then calculate the test statistic, which is the z-score.

The test statistic formula is: z = (x-bar - mu) / (s / sqrt(n))

Using the given values, we have: z = (18.5 - 19) / (3.2 / sqrt(51))

By calculating this expression, we find the test statistic to be approximately -0.81. Next, we determine the critical value from the standard normal distribution table at a significance level of 0.05. The critical value is -1.645 for a one-tailed test.

Since the test statistic (-0.81) is greater than the critical value (-1.645), we fail to reject the null hypothesis. This means the data does not provide sufficient evidence to conclude that the average length of a trout caught in Pyramid Lake is less than 19 inches.