The following prices, in dollars, of 7.5-cubic-foot refrigerators were recorded from a random sample. 314 305 344 283 285 310383285300300 A consumer organization reports that the mean price of 7.5-cubic-foot refrigerators is greater than $300. Do the data provide convincing evidence of this claim? Use the α = 0.05 level of significance and assume the population is normally distributed.

The degrees of freedom are given by:

And the p value would be given by:

Since the p value is higher than the significance level of 0.05 we don't have enough evidence to conclude that the true mean is significantly higher than $300 because we FAIL to reject the null hypothesis.

Step-by-step explanation:

Information given

314 305 344 283 285 310 383 285 300 300

We can calculate the sample mean and deviation with the following formula:

represent the sample mean      

represent the standard deviation for the sample      

sample size      

represent the value to test

represent the significance level

t would represent the statistic

represent the p value

Hypothesis to test

We want to verify if the true mean is greater than 300, the system of hypothesis would be:      

Null hypothesis:      

Alternative hypothesis:      

The statistic is given by:

(1)      

Replacing the info given we got:

The degrees of freedom are given by:

And the p value would be given by:

Since the p value is higher than the significance level of 0.05 we don't have enough evidence to conclude that the true mean is significantly higher than $300 because we FAIL to reject the null hypothesis.