A researcher claims that a post-lunch nap decreases the amount of time it takes males to sprint 20 meters after a night with only 4 hours of sleep. The table shows the amounts of time (in seconds) it took for 10 males to sprint 20 meters after a only 4 hours of sleep when they did not take a post-lunch nap and when they did take a post-lunch nap. At a= 0.10, is there enough evidence to support the researcher's daim? Assume the samples are random and dependent, and the population is normally distributed. Complete parts (a) through (e) below. ra night with Maie Sprint time (without hap) Sprint time (with nap) 3.91 3.99 3.95 3.92 3.92 3.79 3.82 3.89 3.81 3.79 12 3 4 56 7 89 10 4.04 4.06 4.01 3.97 3.94 3.91 3.97 4.02 3.93 3.91

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A researcher claims that a post-lunch nap decreases the amount of time it takes males to sprint 20 meters after a night with only 4 hours of sleep. The table shows the amounts of time (in seconds) it took for 10 males to sprint 20 meters after a night with only 4 hours of sleep when they did not take a post-lunch nap and when they did take a post-lunch nap. At α = 0.10, is there enough evidence to support the researcher's claim? Assume the samples are random and dependent, and the population is normally distributed. Complete parts (a) through (c) below.

| Male | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|------|---|---|---|---|---|---|---|---|---|----|
| **Sprint time (without nap)** | 4.01 | 4.06 | 4.01 | 3.97 | 3.94 | 3.94 | 3.93 | 3.92 | 3.89 | 3.87 |
| **Sprint time (with nap)** | 3.91 | 3.99 | 3.85 | 3.92 | 3.92 | 3.87 | 3.89 | 3.81 | 3.79 | 3.74 |

(a) Identify the claim and state \( H_0 \) and \( H_a \).

What is the claim?

A. A post-lunch nap decreases the amount of time it takes males to sprint 20 meters.  
B. A night with only 4 hours of sleep increases the amount of time it takes males to sprint 20 meters.  
C. A post-lunch nap increases the amount of time it takes males to sprint 20 meters.  
D. A night with only 4 hours of sleep decreases the amount of time it takes males to sprint 20 meters.

Let \( d \) be the hypothesized mean of the difference in the sprint times (without nap – with nap). What are \( H_0 \) and \( H_a \)?

A. \( H_0: \mu_d \le 0 \)  
   \( H_a: \mu_d > 0 \)  

B
Transcribed Image Text:**Transcription:** --- A researcher claims that a post-lunch nap decreases the amount of time it takes males to sprint 20 meters after a night with only 4 hours of sleep. The table shows the amounts of time (in seconds) it took for 10 males to sprint 20 meters after a night with only 4 hours of sleep when they did not take a post-lunch nap and when they did take a post-lunch nap. At α = 0.10, is there enough evidence to support the researcher's claim? Assume the samples are random and dependent, and the population is normally distributed. Complete parts (a) through (c) below. | Male | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |------|---|---|---|---|---|---|---|---|---|----| | **Sprint time (without nap)** | 4.01 | 4.06 | 4.01 | 3.97 | 3.94 | 3.94 | 3.93 | 3.92 | 3.89 | 3.87 | | **Sprint time (with nap)** | 3.91 | 3.99 | 3.85 | 3.92 | 3.92 | 3.87 | 3.89 | 3.81 | 3.79 | 3.74 | (a) Identify the claim and state \( H_0 \) and \( H_a \). What is the claim? A. A post-lunch nap decreases the amount of time it takes males to sprint 20 meters. B. A night with only 4 hours of sleep increases the amount of time it takes males to sprint 20 meters. C. A post-lunch nap increases the amount of time it takes males to sprint 20 meters. D. A night with only 4 hours of sleep decreases the amount of time it takes males to sprint 20 meters. Let \( d \) be the hypothesized mean of the difference in the sprint times (without nap – with nap). What are \( H_0 \) and \( H_a \)? A. \( H_0: \mu_d \le 0 \) \( H_a: \mu_d > 0 \) B
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