Question

select the correct answer from each drop-down menu.

amélie runs a bakery. she wants to find out whether her cake sales are affected by the weather conditions. she recorded the daily temperature and the number of cakes she sold on different days of the year. the table shows the data she gathered.

\

$$\begin{tabular}{|c|c|} \\hline daily temperature (\\(^{\\circ}\\text{f}\\)) & cakes sold \\\\ \\hline 42 & 39 \\\\ \\hline 45 & 52 \\\\ \\hline 48 & 31 \\\\ \\hline 54 & 61 \\\\ \\hline 59 & 72 \\\\ \\hline 62 & 35 \\\\ \\hline 64 & 61 \\\\ \\hline 65 & 34 \\\\ \\hline 67 & 58 \\\\ \\hline 75 & 45 \\\\ \\hline 84 & 24 \\\\ \\hline \\end{tabular}$$

the correlation coefficient is close to choose an answer.
based on this information, we can conclude that amélies cake sales are choose an answer affected by the daily temperature.

Explanation:

Calculate the correlation coefficient

Let \(x\) represent the Daily Temperature (\(^\circ\text{F}\)) and \(y\) represent the Cakes Sold.
The data points \((x, y)\) are:
\((42, 39), (45, 52), (48, 31), (54, 61), (59, 72), (62, 35), (64, 61), (65, 34), (67, 58), (75, 45), (84, 24)\)

Number of data points \(n = 11\).

Calculate the summary statistics:

$$
LATEXBLOCK0
$$

Apply the Pearson correlation coefficient formula:

$$
LATEXBLOCK1
$$

Determine the strength of the relationship

The correlation coefficient \(r \approx 0.29\) is positive but very weak (close to \(0\)).
Therefore, the correlation coefficient is close to \(0.29\) (or approximately \(0.30\)), indicating that Amélie's cake sales are not affected (or at most weakly/not strongly affected) by the daily temperature. Looking at the standard options for such questions, the correlation coefficient is close to \(0.29\) (or \(0.3\)), and the sales are "not" affected.

Answer:

Question 1

The correlation coefficient is close to <blank>\(0.29\)</blank>.

Question 2

Based on this information, we can conclude that Amélie's cake sales are <blank>not</blank> affected by the daily temperature.