According to​ www.marketingcharts.com/, the average 

1818dash–2424​-year 

old has old has 

575575 

Facebook friends. A student wanted to test if the mean number is higher at his school and collected the accompanying survey data. A bootstrap test of the hypotheses 

Upper H 0 : mu equals 575H0: μ=575 

and 

Upper H Subscript Upper A Baseline : mu greater than 575HA: μ>575 

produced the accompanying distribution​ (shifted to center the histogram at the hypothesized mean of 

575575​). 

Complete parts a and b below.

Let's analyze this step-by-step. You are given a hypothesis test setup where a student is testing if the mean number of Facebook friends is higher at his school than the population mean of 575 friends for people aged 18-24, according to the data source. Here are the hypotheses:

- **Null Hypothesis (H₀)**: The mean number of Facebook friends at the school is equal to 575.  
  \( H₀: \mu = 575 \)

- **Alternative Hypothesis (Hₐ)**: The mean number of Facebook friends at the school is greater than 575.
  \( Hₐ: \mu > 575 \)

The bootstrap test involves resampling the data to create a distribution centered at the hypothesized mean (575), then assessing how many sample means exceed this value. Let’s address the specific parts below:

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### Part (a)
**Describe what the p-value represents in the context of this test.**

The **p-value** in this context represents the probability of obtaining a sample mean as extreme or more extreme than the observed sample mean (calculated from the school data), under the assumption that the null hypothesis is true (i.e., that the mean number of friends at the school is indeed 575). 

In other words, it quantifies how unusual the observed result would be if the true mean number of Facebook friends was 575. A smaller p-value indicates stronger evidence against the null hypothesis.

---

### Part (b)
**Explain what it would mean to reject the null hypothesis in this context.**

To **reject the null hypothesis** means that we have sufficient evidence to conclude that the mean number of Facebook friends for students at this particular school is significantly greater than 575. This would suggest that students at the school tend to have more Facebook friends on average than the broader age group.

If the p-value is less than the significance level (typically 0.05), we would reject the null hypothesis and conclude that there is significant evidence supporting that the mean is indeed higher than 575.

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Do you have any more details or questions?

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### Further Related Questions
1. What factors might affect the number of Facebook friends a student has at this school compared to the national average?
2. How would the results change if we used a two-tailed test instead of a one-tailed test?
3. What assumptions are made when conducting a bootstrap test?
4. How would the conclusion be affected if the p-value was close to 0.05?
5. How could increasing the sample size of students surveyed impact the results?

### Tip
In hypothesis testing, always clearly define the significance level (\(\alpha\)) before analyzing the p-value to make an informed decision on whether to reject the null hypothesis.

According to www.marketingcharts.com, the average 18–24-year-old has 575 Facebook friends. A student wanted to test if the mean number is higher at his school and collected the accompanying survey data. A bootstrap test of the hypotheses H0: μ = 575 and HA: μ > 575 produced the accompanying distribution (shifted to center the histogram at the hypothesized mean of 575). Complete parts a and b below.

Analyze the hypothesis test to determine if the mean number of Facebook friends for 18–24-year-olds is higher at a particular school than the reported average of 575. This example covers hypothesis testing concepts, including bootstrap methods and p-value interpretation. Suitable for college-level statistics.

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