Researchers in the UK designed a study to determine if skin wrinkled from submersion in water performed better at handling wet objects.¹ They gathered 20 participants and had each move a set of wet objects and a set of dry objects before and after submerging their hands in water for 30 minutes (order of trials was randomized). The response is the time (seconds) it took to move the specific set of objects with wrinkled hands minus the time with unwrinkled hands. The mean difference for moving dry objects was 0.85 seconds with a standard deviation of 11.5 seconds. The mean difference for moving wet objects was -15.1 seconds with a standard deviation of 13.4 seconds. ¹Kareklas, K., Nettle, D., and Smulders, T.V., "2013 Waterinduced finger wrinkles improve handling of wet objects." Biol. Lett vol 9 (2013). (a) Perform the appropriate test to determine if the wrinkled hands were significantly faster than unwrinkled hands at moving dry objects.

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Researchers in the UK designed a study to determine if skin wrinkled from submersion in water performed better at handling wet
objects. They gathered 20 participants and had each move a set of wet objects and a set of dry objects before and after submerging
their hands in water for 30 minutes (order of trials was randomized). The response is the time (seconds) it took to move the specific set
of objects with wrinkled hands minus the time with unwrinkled hands. The mean difference for moving dry objects was 0.85 seconds
with a standard deviation of 11.5 seconds. The mean difference for moving wet objects was -15.1 seconds with a standard deviation
of 13.4 seconds.
¹Kareklas, K., Nettle, D., and Smulders, T.V., "2013 Waterinduced finger wrinkles improve handling of wet objects." Biol. Lett vol 9
(2013).
(a) Perform the appropriate test to determine if the wrinkled hands were significantly faster than unwrinkled hands at moving dry
objects.
State the null and alternative hypotheses.
Use μ₁ for μ in the response area.
Ho:
II
(b) Calculate the relevant test statistic.
p-value =
Round your answer to two decimal places.
t-statistic =
μ
i
i
(c) Find the p-value.
Round your answer to three decimal places.
vs Ha:¦
:: I₂
4
:: p
₂
:: P
:: P₁
:: P₂
P₁
:: P₂
r
:: 0
p
I
Transcribed Image Text:Researchers in the UK designed a study to determine if skin wrinkled from submersion in water performed better at handling wet objects. They gathered 20 participants and had each move a set of wet objects and a set of dry objects before and after submerging their hands in water for 30 minutes (order of trials was randomized). The response is the time (seconds) it took to move the specific set of objects with wrinkled hands minus the time with unwrinkled hands. The mean difference for moving dry objects was 0.85 seconds with a standard deviation of 11.5 seconds. The mean difference for moving wet objects was -15.1 seconds with a standard deviation of 13.4 seconds. ¹Kareklas, K., Nettle, D., and Smulders, T.V., "2013 Waterinduced finger wrinkles improve handling of wet objects." Biol. Lett vol 9 (2013). (a) Perform the appropriate test to determine if the wrinkled hands were significantly faster than unwrinkled hands at moving dry objects. State the null and alternative hypotheses. Use μ₁ for μ in the response area. Ho: II (b) Calculate the relevant test statistic. p-value = Round your answer to two decimal places. t-statistic = μ i i (c) Find the p-value. Round your answer to three decimal places. vs Ha:¦ :: I₂ 4 :: p ₂ :: P :: P₁ :: P₂ P₁ :: P₂ r :: 0 p I
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