The table shows the overall scores and the prices per gallon for seven randomly selected interior paints. The overall score represents hiding, surface smoothness, and resistance to staining, scrubbing, gloss change, sticking, mildew, and fading. 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 46 73 64 56 94 86 50 Price per gallon (in dollars) 24 40 25 24 40 38 26