Math Problem Statement

Netflix: A study conducted by the technology company TiVo showed that the mean time spent per day browsing the video streaming service Netflix for something to watch was 20.1 minutes. Assume the standard deviation is σ = 7. Suppose a simple random sample of 103 visits taken this year has a sample mean of x̄ = 22.1 minutes. A social scientist is interested to know whether the mean time browsing Netflix has changed. Use the α = 0.05 level of significance and the critical value method with the table.

Solution

Let's analyze the question and address it step by step.

Problem Breakdown:

  • Given:
    • Previous mean time μ=20.1\mu = 20.1 minutes.
    • Sample size n=103n = 103.
    • Sample mean xˉ=22.1\bar{x} = 22.1 minutes.
    • Population standard deviation σ=7\sigma = 7.
    • Significance level α=0.05\alpha = 0.05.
  • Goal: Determine if the mean time spent browsing Netflix has changed (two-tailed test).

Part (a) Null and Alternate Hypotheses

  • The null hypothesis (H0H_0): There is no change in the mean time spent browsing Netflix. H0:μ=20.1H_0: \mu = 20.1
  • The alternate hypothesis (H1H_1): The mean time spent browsing Netflix has changed. H1:μ20.1H_1: \mu \neq 20.1

This is a two-tailed test since the question is testing whether the mean has changed, rather than specifically increased or decreased.


Let me know if you need further assistance or details on hypothesis testing steps.

Related Questions:

  1. What is the next step after stating the hypotheses in hypothesis testing?
  2. How do we calculate the test statistic for this scenario?
  3. What does the critical value method involve, and how does it relate to the significance level?
  4. How can we interpret the results to decide whether to reject H0H_0?
  5. What is the role of the sample size nn in hypothesis testing?

Tip:

Always start hypothesis testing by clearly defining the null and alternate hypotheses and ensure they align with the problem's question.

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Math Problem Analysis

Mathematical Concepts

Hypothesis testing
Two-tailed tests
Significance level
Critical value method

Formulas

z = (x̄ - μ) / (σ / √n)

Theorems

Central Limit Theorem
Critical value approach

Suitable Grade Level

College level or Advanced High School Statistics