Since 2008 Airbnb has been popular among hosts and travelers due to unique travelling possibilities it offers. A marketing researcher is interested in understanding average price per night for a private room for neighborhoods around New York city.

He collected data on the rental price per night for 45 private room rentals in 5 neighborhoods around New York city (Manhattan, Bronx, Brookline, Queens, and Staten Island).

He then used a one-way ANOVA model to test whether the mean rental price per night for a private room around New York city (NYC) depends on the neighborhood.

The incomplete ANOVA table is given below.

1. Write down the null and the alternative hypotheses for testing whether or not the mean price per night for a NYC private room depends on the neighborhood. Clearly define any parameters you might use
2. Compute the 3 degrees of freedoms missing in the ANOVA table (i.e. DF for neighborhood, error DF and total DF)
3. Compute Error Sums of squares missing (i.e. AdjSS for Error)
4. Compute the missing Mean squares (i.e. error MS and MS for neighborhood) and the F-value
5. Using the ANOVA table test at 5% significance level the hypothesis in part (1). Write down the conclusion in the context of the problem.
6. The output for Tukey comparisons is given below. Based on the output, is the mean price per night for a private room in Queens if different from Bronx at 5% significant level? Explain your answer.

Factor Information Factor Levels Values neighborhood 5 Bronx, Brooklyn, Manhattan, Queens, Staten Island Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value neighborhood 69367 0.000 Error Total 70524 Model Summary S R-sq R-sq(adj) R-sq(pred) 5.37904 98.36% 98.19% 97.92%Grouping Information Using the Tukey Method and 95% Confidence neighborhood N Mean Grouping Manhattan 9 198.03 A Brooklyn 9 125.89 B Staten Island 114.92 C Queens 9 99.41 D Bronx 9 84.78 E Means that do not share a letter are significantly different