Question

Need Help checking my t value and critical t!

What is the optimal time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic. The Navy defines the "optimal time" to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let x = depth of dive in meters, and let y = optimal time in hours. A random sample of divers gave the following data.

x	14.1	23.3	28.2	38.3	51.3	20.5	22.7
y	2.68	2.18	1.48	1.03	0.75	2.38	2.20

(f) Use a 1% level of significance to test the claim that β < 0. (Round your answers to two decimal places.)

I got: t = -7.70

critical t = 3.37 (one-tailed area?)

(g) Conclusion:

a. Reject the null hypothesis. There is insufficient evidence that β < 0

b. Fail to reject the null hypothesis. There is sufficient evidence that β < 0.  

c. Reject the null hypothesis. There is sufficient evidence that β < 0. (Is this correct)

d. Fail to reject the null hypothesis. There is insufficient evidence that β < 0.

Answer 1

The slope from the given data will be -0.0559

We calculate Sb = 0.007262

(b) The Hypothesis:

H0: = 0

Ha: < 0

This is a left tailed test

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The Test Statistic:

The critical value (Left Tailed) for df -= n - 2 = -3.36 (Please note you have taken the positive critical value)

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Since t test is < t critical

Option (c) Reject the Null Hypothesis. There is sufficient evidence that < 0.