Math Problem Statement

In 2015, the average time spent watching streaming services was 25.2 minutes per day. A consumer research company believes that the average time is different today. To test this claim, a sample of 36 households was surveyed, and their average time spent watching streaming is provided. The data consists of 36 time observations (in minutes), which are the times each household spent watching streaming content. Some of the values are: [ 29.27, 23.95, 37.79, 22.46, 23.61, ...].

Solution

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Problem Overview:

In 2015, the average time spent watching streaming services was 25.2 minutes per day. A consumer research company believes that the average time is different today. To test this claim, a sample of 36 households was surveyed, and their average time spent watching streaming is provided.

Data:

The data consists of 36 time observations (in minutes), which are the times each household spent watching streaming content. Some of the values are: 29.27,23.95,37.79,22.46,23.61,29.27, 23.95, 37.79, 22.46, 23.61, \dots

Hypothesis Testing:

  • Null Hypothesis (H₀): The average time spent watching streaming is still 25.2 minutes. H0:μ=25.2H_0: \mu = 25.2

  • Alternative Hypothesis (H₁): The average time spent watching streaming is different from 25.2 minutes. H1:μ25.2H_1: \mu \neq 25.2

Tasks:

  1. Calculate the test statistic: This involves using the sample mean and sample standard deviation to perform a t-test.
  2. Calculate the p-value: This helps in determining if the result is statistically significant.
  3. Make a decision: Based on the p-value, decide whether to reject the null hypothesis.
  4. Conclusion: Conclude whether there is enough evidence to support the claim that the average time is different from 25.2 minutes.

Next Steps:

You need to calculate the sample mean, sample standard deviation, and then compute the test statistic and p-value.

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
t-Test
Sample Mean
Standard Deviation

Formulas

t = (x̄ - μ) / (s / √n)
p-value calculation based on t-distribution

Theorems

Central Limit Theorem
Student's t-distribution

Suitable Grade Level

College level (Statistics)