Question

Q7) A hypothesis test is to be performed with a Null hypothesis  and an alternative hypothesis  , the population standard deviation is σ=3.0, the sample size is 30, and the significance level is α=0.025.

1. What is a type I error?                                                                                  (1 mark)

2. What is the chance of making a type I error in the above test?

  (1 mark)

3. What is a Type II error?                                                                                (1 mark)

4. What value would the sample mean have to be greater than to reject Ho?

    (2 marks)

5. It is unknown to the technician making the test, but the real value of µ=22. What is the probability that a Type II error occurs?

          (state accurate to 4dp)

(4 marks)

6. In a word, what will happen to the Type II error if the sample size increases to 60 and all else remains unchanged, including the answer to part d)

  (1 mark)

Q8) A neuropsychologist was interested in how Monkeys learn to perform a task. The task was to retrieve a coconut from the opposite side of a river.

15 wild monkeys were assigned to one of three conditions where they were shown how to retrieve a coconut by using one of three different techniques.

The times taken for the monkeys to retrieve the coconut is given below in minutes.

Perform an ANOVA hypothesis test to answer the question: Are there significant differences in the speed of coconut retrieval between the 3 techniques?

Present your answers with an ANOVA table and follow the full hypothesis testing procedure. Values should all be correct to at least 1 decimal place

	Technique 1	Technique 2	Technique 3
	1 1 7 13 13	7 15 1 8 9	15 8 13 13 6
Means	7	8	11
St-Dev	6	5	3.8079

   

The ANOVA hypotheses are:

H_o: Average times to retrieve a coconut are the same.

H₁: Average time for at least one technique is different from the others.

1. Fill in the seven missing values from the ANOVA table below.

(9 Marks)

(Round the SS and Variance values to 2 decimal places and F-test-statistic to 1 decimal place)

Source	Sum of Squares SS (2 dp accuracy)	DF	Variance (2 dp accuracy)	F-Test (1 dp accuracy)
Between Groups	43.3333
Within Groups
Total		14

2. State the critical value from tables and use this to say whether there is a significant result and whether H_o is rejected or not. Use α=0.05 significance level.

(1 Mark)

Answer 1

7. a). Type I error is error committed while rejecting a null hypothesis when it is true or rejecting a good quality lot. It is also called Producers risk and is also referred to as FALSE POSITIVES. It is denoted by $\alpha$ .

b). In above example, $\alpha$ = 0.025 or we can say that there is 2.5% chance of rejecting Null hypothesis when it is true out of 100%.

c). Type II error is the error committed while accepting an alternative hypothesis when is is false or accepting a bad quality lot. It is also called consumers risk and is also referred as FALSE NEGATIVE. It is denoted by $\beta$ .

d). Here, for testing hypothesis of means, we can obtain the upper and lower limits or interval range of the mean.

We know, the formula is $\overline{x}$ $\pm$ Z$\alpha$/2 * $\sigma/\sqrt{n}$ and we are given the values, for one tailed, z = 1.96, sigma = 3, n = 30. substituting these values, we get $\overline{x}$ $\pm$ 1.0735. So, mean should be greater by 1.0735 to reject Ho.