A random sample of 144 artworks created within the last three years and sold at auction has been selected to study art auction price and prior exhibition. Some of the variables recorded for each artwork are listed below.

Variable	Description
subid	Subject ID
medium	type of artwork
exhibWeeks	the number of weeks the artwork was exhibited before the auction
price	sale price (in thousands)
Import the data set included in the file sample.csv in Excel. To do this, you need to click on the link above and save the data file in a convenient location on your PC (in your browser, File and Save). Next open Excel, click File in the Menu, select Open and navigate to the file you previously saved – or simply double-click on it, Excel should open automatically. Use Excel and/or probTool, and appropriate hypothesis tests, to address the following research questions. Assume all the test assumptions are verified.
Part 1
Is there any difference between paintings and sculptures in the average number of weeks the artworks were exhibited before auction?
Report the absolute value of the test statistic [use at least 14dp]:	 

To determine if there is a difference between the average number of weeks paintings and sculptures were exhibited before auction, we need to conduct a hypothesis test. Specifically, we'll use an independent two-sample t-test (assuming the data is normally distributed or that the sample sizes are large enough to apply the Central Limit Theorem) to compare the means of the two groups: paintings and sculptures.

### Step-by-Step Solution:

1. **Formulate Hypotheses:**
   - Null Hypothesis (\(H_0\)): There is no difference between the average number of weeks paintings and sculptures were exhibited before auction.
     \[
     H_0: \mu_1 = \mu_2
     \]
   - Alternative Hypothesis (\(H_a\)): There is a difference between the average number of weeks paintings and sculptures were exhibited before auction.
     \[
     H_a: \mu_1 \neq \mu_2
     \]
   Here, \(\mu_1\) represents the mean exhibition weeks for paintings, and \(\mu_2\) represents the mean for sculptures.

2. **Calculate the Test Statistic:**
   The formula for the t-statistic in an independent two-sample t-test is:
   \[
   t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}
   \]
   where:
   - \(\bar{x}_1, \bar{x}_2\) are the sample means for paintings and sculptures.
   - \(s_1^2, s_2^2\) are the sample variances for paintings and sculptures.
   - \(n_1, n_2\) are the sample sizes for paintings and sculptures.

3. **Use Excel to Obtain Descriptive Statistics:**
   - Open the `sample.csv` file in Excel.
   - Filter the data by the "medium" variable to separate paintings and sculptures.
   - Calculate the mean, standard deviation, and sample size for the "exhibWeeks" variable for each group (paintings and sculptures).

4. **Compute the t-statistic:**
   Use the values from the descriptive statistics to calculate the t-statistic using the formula provided.

5. **Report the Absolute Value of the Test Statistic:**
   Ensure that the result is reported to at least 14 decimal places.

### Next Steps:
- To perform this test accurately, you will need to input the sample data into Excel, compute the necessary descriptive statistics (mean, standard deviation, sample size), and use the t-test formula to find the test statistic. 

Would you like more guidance on using Excel to calculate these values, or any further details about the hypothesis test? 

### Further Related Questions:
1. What is the p-value associated with the t-test, and how does it compare to the significance level?
2. How do the variances between paintings and sculptures compare? Should we use a pooled or unpooled t-test?
3. What are the assumptions required for conducting an independent two-sample t-test, and are they met in this case?
4. How would the results change if the sample size was larger or smaller?
5. What effect size measure can be used to quantify the difference between the two groups?

#### Tip:
Always check the assumptions of normality and equality of variances when conducting a t-test to ensure the test's validity.

Is there any difference between paintings and sculptures in the average number of weeks the artworks were exhibited before auction? Report the absolute value of the test statistic [use at least 14dp].

Learn how to conduct an independent two-sample t-test to determine if there's a difference in the average number of exhibition weeks between paintings and sculptures. This step-by-step solution explains hypothesis testing, calculates the t-statistic, and reports the test result with precision up to 14 decimal places. Suitable for undergraduate-level statistics students.

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