A fisherman wants to determine if the mean weight of crappie in a lake exceeds 3

Question

A fisherman wants to determine if the mean weight of crappie in a lake exceeds 35 ounces. He records weights for 15 crappie and finds the mean weight is 36.301 ounces with a standard deviation of 2.861 ounces. You may assume (accept as true) that the weights for crappie in the lake are normally distributed and the fish he recorded weights for are like a random sample. Complete the steps of the hypothesis test using a 10% level of significance. (1 point each except where indicated.)

Let m be the mean weight of all crappie in the lake.

H0: m = ___ ounces

Decision Rule: Reject Ho if the p-value (probability) is less than or equal to _________ .

The test statistic is calculated to be _______ when rounded to 3 digits after the decimal point.

Based on Ha and the calculated test statistic value, what is the probability (or p-value) from Table T? Give this value rounded to 4 decimal places. __________

Based on the decision rule and the probability, the decision should be which of these? (Circle the correct decision)

reject H0

fail to reject H0

Summary:

For the given level of significance, there ________ (enter is or is not) significant evidence to conclude the mean weight of crappie in the lake exceeds 35 ounces.

Explanation / Answer

H0: m = 35 ounces

Ha: m > 35 ounces

Since sample size is 15, which is less than 30, so we conduct a t-test here.

Critical t-score for a system with 15-1 = 14 degrees of freedom with 10% significance level is:

tcritical = 1.345

Using t-table we conclude that:

Reject Ho if the p-value (probability) is less than or equal to 0.1

Data given:

Sample mean, X' = 36.301

Sample size, n = 15

Sample s.d., S = 2.861

Calculating the t-statistic value:

tscore = (X' - m) / (S/n0.5) = (36.301 - 35) / (2.861/150.5) = 1.761

From the t-table, we get the p-value as: 0.0500

Based on decision rule and probability, reject Ho.

Summary:

For the given level of significance, there is significant evidence to conclude the mean weight of crappie in the lake exceeds 35 ounces.

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