Question

Question 3: Test of Significance

Exit time from a labyrinth: In a lab is tested the time mice need to find their way out through a labyrinth. The mean time of a population of 100 mice is 18 seconds. A researcher thinks that a louder noise would make mice to complete the labyrinth faster. She tests this with 10 mice and proves how long the mice would need to go out with the noise as stimulus. The sample mean is ?̅ = 16.5 and s= 10.

a) What is the null and alternative hypothesis?

b) Calculate the value of z test statistics and the P-Value

c) According to the P- Value, it is necessary to repeat the test once again? Justify your answer using the significance levels 0.01< ? < 0.05

Please answer all questions for thumbs up!

Answer 1

a) As we are testing here whether a louder noise would make mice to complete the labyrinth faster, therefore the null and the alternative hypothesis here are given as:

b) The test statistic here is computed as:

As this is a one tailed test, for n - 1 = 9 degrees of freedom, the p-value here is obtained from t distribution tables here as:

p = P( t₉ < -0.4743) = 0.3233

Therefore 0.3233 is the required p-value here.

c) As the p-value here is very high, and certainly higher than 0.05 at which we are doing the test, therefore the test is not significant here and we cannot reject the null hypothesis here. Therefore we dont have sufficient evidence right now that a louder noise would make mice to complete the labyrinth faster. Therefore the test is to be repeated here.