The table shows the overall scores and the prices for six randomly selected video disk players. The overall score is based mainly on picture quality. At \(\alpha=0.10\), can you conclude that there is a significant correlation between the overall score and the price?

Use the Spearman rank correlation coefficient to test the claim by doing the following.

(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.

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

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Overall score 93 91 90 87 85 69 500 300 500 150 25 Price (in dollars) 500 130