Math Problem Statement

A researcher wants to test whether the average weight of a certain species of fish is 2 kg. A sample of 20 fish is taken, yielding a sample mean weight of 1.8 kg with a standard deviation of 0.5 kg.

Solution

Let's break down and solve this question step by step.

Question 6 Summary:

The researcher is testing whether the average weight of a species of fish is 2 kg. A sample of 20 fish is taken, with a sample mean of 1.8 kg and a standard deviation of 0.5 kg. The test requires:

  • (a) The null and alternative hypotheses.
  • (b) The t-statistic.
  • (c) The critical t-value at a significance level of 0.01 (two-tailed).
  • (d) Determination of whether to reject the null hypothesis based on the t-statistic and critical value.

Part (a) - Null and Alternative Hypotheses:

  • Null Hypothesis (H₀): The

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
t-distribution

Formulas

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

Theorems

t-distribution
Hypothesis Testing

Suitable Grade Level

Undergraduate Statistics

Related Recommendation

Hypothesis Test for Fish Weight with a Two-Tailed t-Test

Hypothesis Testing: Mean Weight of Blue Catfish in John H. Kerr Reservoir

Hypothesis Test for Biologist's Claim About Animal Weight

Hypothesis Testing with Independent Samples t-test for Fish Weight Comparison

One-Tailed t-Test to Determine if Population Mean is Less Than 20