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)...

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=0.05​, 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​ (e) below.

Extracted text: 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 mete 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 a = 0.05, 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 (e) below. Male 2 3 4 5 6 7 8 9 10 P Sprint time (without nap) Sprint time (with nap) 4.08 3.96 3.99 3.93 3.92 4.02 4.05 4.07 3.95 |3.91 3.95 3.89 3.90 3.88 3.90 3.92 3.90 3.92 3.84 3.76 (a) Identify the claim and state Ho and Ha. What is the claim? O A. A post-lunch nap increases the amount of time it takes males to sprint 20 meters. O B. Anight with only 4 hours of sleep decreases the amount of time it takes males to sprint 20 meters. O C. Anight with only 4 hours of sleep increases the amount of time it takes males to sprint 20 meters. O D. A post-lunch nap decreases the amount of time it takes males to sprint 20 meters. Let Hd be the hypothesized mean of the difference in the sprint times (without nap - with nap). What are H, and H,? O A. Ho: Hd sd Ha: Hd >d O B. Ho: Hd 2d O C. Ho: Hd #0 Hai Hd = 0 Hai Hd O D. Ho: Hd s0 Ha: Hd >0 O E. Ho: Hd 20 Ha: Hd <0 o="" f.="" ho:="" hd="0" ha:="" ha="" #0="" (b)="" find="" the="" critical="" value(s)="" and="" identify="" the="" rejection="" region(s).="" select="" the="" correct="" choice="" below="" and="" fill="" in="" any="" answer="" boxes="" to="" complete="" your="" choice.="" (round="" to="" three="" decimal="" places="" as="" needed.)="" a.="">< or="" t=""> О В. t< с.="" t=""> (c) Calculate d and d = (Round to three decimal places as needed.) Calculate sd. Sa = (Round to three decimal places as needed.) %3D (d) Find the standardized test statistic t. t= (Round to three decimal places as needed.) (e) Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. V the null hypothesis. There V enough evidence to V the claim that a the amount of time it takes males to sprint 20 meters.