Vacuum Cleaners The table shows the overall scores and the prices for a random sample of 12 different models of vacuum cleaners. The overall score represents cleaning, airflow, handling, noise, and emissions. At \(\alpha=0.10\), can you conclude that there is a significant correlation between the overall score and the price?

(a) identify the claim and state \(H_{0}\) and \(H_{a}\),

(b) find the critical value,

(c) find the test statistic \(r_{s}\),

(d) decide whether to reject or fail to reject the null hypothesis, and

(e) interpret the decision in the context of the original claim.

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Overall score 65 71 69 47 55 38 Price (in dollars) 150 200 550 350 470 90 90 Overall score 47 47 47 57 34 65 Price (in dollars) 80 130 210 190 300 260