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WILL GIVE BRAINLIEST TO PERSON WHO ANSWERS CORRECTLY!!!!! PLEASE HELP ME!!!!!!

A specialty ice cream manufacturer collected data for the number of ice creams sold each day and the temperature on that day. The data was displayed in the following table.

Ice Creams Sold - 34, 39, 40, 36, 46, 47, 54, 27, 31, 56

Temperature (in °F) - 71.0, 73.8, 74.9, 71.4, 75.0, 76.9, 79.4, 68.6, 70.0, 81.4

What is the best interpretation of the correlation coefficient between the temperature and the number of ice creams sold?

* Because the correlation coefficient is close to -1, the ice cream sales decrease markedly with a rise in temperature.
* Because the correlation coefficient is close to 1, the ice cream sales increase markedly with a rise in temperature.
* Because the correlation coefficient is close to 1, the ice cream sales increase vaguely with a rise in temperature.
* Because the correlation coefficient is close to 0, the ice cream sales decrease vaguely with a rise in temperature.

Respuesta :

B. increase markedly with a rise in temperature.
mathmate
Given the sales list S, and the temperature list T.
S:[34, 39, 40, 36, 46, 47, 54, 27, 31, 56]
T:[71.0, 73.8, 74.9, 71.4, 75.0, 76.9, 79.4, 68.6, 70.0, 81.4]
n=10 = number of observations in each list.

We need the correlation coefficient ρ to select the right choice of answers.

We first calculate the mean μ and standard deviation σ of each list
[tex]\mu_s=\sum_{i=1}^{10}S_i=41.0[/tex]

[tex]\sigma^2_s=\sum_{i=1}^{10}(S_i-\mu_s)^2/n=83[/tex]
[tex]\sigma_s=\sqrt{\sigma^2_s}=\sqrt{83}=9.1104[/tex]

[tex]\mu_t=\sum_{i=1}^{10}T_i=74.24[/tex]
[tex]\sigma^2_t=\sum_{i=1}^{10}(T_i-\mu_t)^2/n=15.4524[/tex]
[tex]\sigma_t=\sqrt{\sigma^2_t}=\sqrt{15.4524}=3.9310[/tex]

We are now ready to calculate the correlation coefficient ρ :
[tex]\rho=\frac{E[(S-\mu_s)(T-\mu_t)]}{\sigma_s*\sigma_t}[/tex]
[tex]=\frac{\sum_{i=1}^{n}[(S_i-\mu_s)(T_i-\mu_t)]/n}{\sigma_s*\sigma_t}[/tex]
[tex]=\frac{\sum_{i=1}^{n}[(S_i-\mu_s)(T_i-\mu_t)]/n}{9.1104*3.9310}[/tex]
[tex]=\frac{35.27}{35.8127}[/tex]=0.9848

Because the correlation coefficient, ρ , is close to one, the ice cream sales increase markedly with a rise in temperature.

Note: 
a correlation close to 1 means both increase (or decrease)
a correlation close to -1 means one increases while the other decreases
correlation close to 0 means one does not quite affect the other.