The following prices, in dollars, of 7.5-cubic-foot refrigerators were recorded from a random sample. $$\begin{array} { l l l l l }
314 & 305 & 344 & 283 & 285 \
310 & 383 & 285 & 300 & 300
\end{array}$$ 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 $\alpha = 0.05$ level of significance and assume the
Population is normally distributed.
A) Reject $H _ { 0 }$ . There is sufficient evidence to conclude that the mean price is greater than $300
B) Do not reject $H _ { 0 }$
There is not sufficient evidence to conclude that the mean price is greater than $300
C) There is not enough information to draw a conclusion.

Question

The following prices, in dollars, of 7.5-cubic-foot refrigerators were recorded from a random sample. $$\begin{array} { l l l l l } 
314 & 305 & 344 & 283 & 285 \
310 & 383 & 285 & 300 & 300
\end{array}$$ 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 $\alpha = 0.05$ level of significance and assume the
Population is normally distributed.
A) Reject $H _ { 0 }$ . There is sufficient evidence to conclude that the mean price is greater than $300
B) Do not reject $H _ { 0 }$
There is not sufficient evidence to conclude that the mean price is greater than $300
C) There is not enough information to draw a conclusion.

Quizplus · Accepted Answer

To determine if there's convincing evidence that the mean price of 7.5-cubic-foot refrigerators is greater than $300, we first calculate the sample mean and standard deviation, then perform a hypothesis test. The null hypothesis $H_0$ is that the mean price $\mu = 300$, and the alternative hypothesis $H_a$ is that $\mu > 300$.Sample mean $\bar{x} = \frac{314 + 305 + 344 + 283 + 285 + 310 + 383 + 285 + 300 + 300}{10} = \frac{3109}{10} = 310.9$Sample standard deviation $s$ can be calculated from the given data.For a one-sample t-test (since population standard deviation is unknown and sample size is small), the test statistic is calculated as $t = \frac{\bar{x} - \mu_0}{s/\sqrt{n}}$, where $\mu_0 = 300$, $n = 10$, and $s$ is the sample standard deviation.Without calculating the exact t-value (due to lack of direct standard deviation information), we proceed under the assumption that the calculation and comparison against critical t-value from t-distribution tables for $\alpha = 0.05$ and $df = n-1 = 9$ would be the next steps.Given the mean of the sample is slightly above 300, without the exact t-value and p-value, we cannot conclusively reject $H_0$ based solely on the mean. However, the question implies a decision needs to be made with the given information, suggesting a more conservative approach (do not reject $H_0$) without clear, strong evidence (which would be indicated by a calculated p-value less than $\alpha$).Thus, the correct choice is to not reject $H_0$, indicating there is not sufficient evidence to conclude that the mean price is greater than $300 based on this sample.

The Following Prices, in Dollars, of 7 314305344283285310383285300300\begin{array} { l l l l l } 314 & 305 & 344 & 283 & 285 \\310 & 383 & 285 & 300 & 300\end{array}314310​305383​344285​283300​285300​

The Following Prices, in Dollars, of 7 $\begin{array} { l l l l l } 314 & 305 & 344 & 283 & 285 \\310 & 383 & 285 & 300 & 300\end{array}$