11) A psychology researcher wants to test the ability of rats to navigate a maze

Question

11) A psychology researcher wants to test the ability of rats to navigate a maze. Mazes are classified according to difficulty, as measured by the mean length of time it takes for rat to find the food at the end. She needs a maze that will take an average of one minute to solve. She constructs a maze and then tests it using 16 rats. Their mean time was x = 63.6 seconds. Assume the standard deviation of the times is = 9 seconds. What is the value of test statistic z for her test of H0: = 60 versus Ha: 60? Give your answer correct to one decimal place.

12) A company manufactures U-100 insulin syringes designed to contain 1 milliliter (ml) of a solution containing insulin. The actual distribution of solution volumes in these syringes is Normal, with mean µ and standard deviation = 0.05 ml. We randomly select 8 syringes and measure the volume of solution in each. The results of these 8 measurements (all in ml) are:

1.05

1.04

1.06

1.01

0.98

0.98

1.03

0.99

We will test H0 = 1 versus Ha: 1. Use your calculator to perform the appropriate test. The P-value is

0.161.

0.989.

0.018.

0.322.

1.05

1.04

1.06

1.01

0.98

0.98

1.03

0.99

Explanation / Answer

Answer to question # 11)

Sample size n = 16

x bar = 63.6

Population Standard deviation SD = 9

M = 60

It is a two tailed test

.

Formula of test statistic Z is:

z = (x bar - M) / (s/sqrt(n))

.

On plugging the vlaues we get:

z = (63.6 -60) / (9/sqrt(16))

z = 3.6 / 2.25

z = 1.6

.

P Value can be obtained from the Z table

P value = 2 * (1 - 0.9452)

P value = 0.1096

.

[0.9452 is the area to the left of z = 1.6 , we need the area under the right tail , so we subtract 0.9452 by 1. this gives us the area under the right tail. Since it is a two tailed test , we get the same area under the left tail as well, so we mulptiply the area under the right tail by 2, to get the exact P value]

.

Inference: P value 0.1096 > alpha 0.05 , we fail to reject the null

.

Conclusion: thus the time taken is 60 Seconds

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