The table shows the overall scores and the prices for a random sample of nine different models of elliptical exercise machines. The overall score represents the ergonomics, exercise range, ease of use, construction, heart-rate monitoring, and safety. At \(\alpha=0.05\), 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 77 75 73 71 Price (in dollars) 3700 1700 1300 900 Overall score 66 66 64 62 58 Price (in dollars) 1000 1400 1800 1000 700