Question

Experiments on learning in animals sometimes measure how long it takes a mouse to find its way through a maze. Long experience indicates that the mean time is 20 seconds for one particular maze.A researcher thinks that playing loud rap music will, on average, cause mice to take longer to complete the maze. (a) State the null and alternative hypothesis in this case. Define (in words) the parameter of interest in this case. A total of 12 mice attempted the maze while loud music was being played. The mea n and standard deviation of the times to complete the maze are given below. y=22.40 seconds S= 3.58 seconds (b) Compute the value for the test statistic (to) in this case and use the t table to find bounds on the corresponding p-value. (c) Can you reject the null hypothesis at the 5% level of significance? xplain (d) Write a conclusion in the context of the problem. (e) Find a 90% confidence interval for the mean time for mice to complete the maze with the loud rap music.

Answer 1

(a) Here y = 22.40 secons

and S = 3.58 seconds

the hypothesis are

Null Hypothesis : H₀ : Louder rap music will, on average, cause mice to dont take longer to complete the maze.

Alternative Hypothesis : H_a : Louder rap music will, on average, cause mice to take longer to complete the maze.

(b) Here test statistic

t = 22.40/3.58 = 6.257

Here the bounds to find the t table is from p value from 0.0001 to 0.01.

(c) Here we will reject the null hypothesis at 5% level of significance.

(d) Here we conclude that the loud rap music will, on average, will cause mice to take longer to complet the maze.

(e) 90% confidence interval = y +- t_critical S = 22.40 +- 1.729 * 3.58

= (16.21 seconds, 28.59 seconds)