|(a) State the null hypothesis H and the alternative hypothesis H,. H. :0 Hị :0 | (b) Determine the type of test statistic to use. (Choose one) ▼ O=0 OSO |(c) Find the value of the test statistic. (Round to three or more decimal places.) OO |(d) Find the p-value. (Round to three or more decimal places.) (e) Can we conclude that the mean puzzle-solving times for crows is less than the mean puzzle-solving times for sparrows? O Yes O No

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Chapter1: Combinatorial Analysis
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A cognitive scientist wants to test whether there is any difference in puzzle-solving abilities between crows and sparrows. Independent samples of eleven crows
and fourteen sparrows were chosen at random. The crows took a mean of 34 minutes to solve a certain puzzle, with a standard deviation of 5.1 minutes. The
sparrows took a mean of 35 minutes to solve the same puzzle, with a standard deviation of 5.9 minutes.
Assume that the two populations of completion times are normally distributed, and that the population variances are equal.
Can we conclude, at the 0.05 level of significance, that u,, the mean puzzle-solving times for crows, is less than u,, the mean puzzle-solving times for
sparrows?
Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of
formulas.)
Transcribed Image Text:A cognitive scientist wants to test whether there is any difference in puzzle-solving abilities between crows and sparrows. Independent samples of eleven crows and fourteen sparrows were chosen at random. The crows took a mean of 34 minutes to solve a certain puzzle, with a standard deviation of 5.1 minutes. The sparrows took a mean of 35 minutes to solve the same puzzle, with a standard deviation of 5.9 minutes. Assume that the two populations of completion times are normally distributed, and that the population variances are equal. Can we conclude, at the 0.05 level of significance, that u,, the mean puzzle-solving times for crows, is less than u,, the mean puzzle-solving times for sparrows? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)
(a) State the null hypothesis H, and the alternative hypothesis H,.
H, :0
H :0
(b) Determine the type of test statistic to use.
(Choose one) ▼
O=0
OSO
(c) Find the value of the test statistic. (Round to three or more decimal places.)
O<O
(d) Find the p-value. (Round to three or more decimal places.)
(e) Can we conclude that the mean puzzle-solving times for crows is less
the mean puzzle-solving times for sparrows?
han
O Yes O No
Transcribed Image Text:(a) State the null hypothesis H, and the alternative hypothesis H,. H, :0 H :0 (b) Determine the type of test statistic to use. (Choose one) ▼ O=0 OSO (c) Find the value of the test statistic. (Round to three or more decimal places.) O<O (d) Find the p-value. (Round to three or more decimal places.) (e) Can we conclude that the mean puzzle-solving times for crows is less the mean puzzle-solving times for sparrows? han O Yes O No
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