The data provides convincing evidence to support the consumer organization's claim that the mean price of 7.5-cubic-foot refrigerators is greater than $300.
Given the sample data, sample mean (310.9), and sample variance (966.3222), we can perform a hypothesis test to determine whether there is enough evidence to support the consumer organization's claim that the mean price of 7.5-cubic-foot refrigerators is greater than $300.
Step 1: State the Hypothesis
Null Hypothesis (H0): μ ≤ 300
Alternative Hypothesis (Ha): μ > 300
Step 2: Set the Significance Level
α = 0.05
Step 3: Calculate the Test Statistic
We will use a t-test since the population variance is unknown. The t-statistic is calculated as follows:
t = (x - μ0) / √(s^2 / n)
where:
x = sample mean (310.9)
μ0 = hypothesized mean (300)
s^2 = sample variance (966.3222)
n = sample size (10)
Plugging in the values, we get:
t = (310.9 - 300) / √(966.3222 / 10) ≈ 2.38
Step 4: Find the P-value
The P-value is the probability of obtaining a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true. We can find the P-value using a t-distribution table or statistical software.
Using a t-distribution table with df = 9 (degrees of freedom = n - 1), we find that the P-value is approximately 0.027.
Step 5: Make a Decision
Since the P-value (0.027) is less than the significance level (0.05), we reject the null hypothesis. This means that there is enough evidence to conclude that the mean price of 7.5-cubic-foot refrigerators is greater than $300.