Answer to Question #197386 in Statistics and Probability for snoopmon

Question

State the null and the alternative hypothesis in words and in symbols. State whether the test is directional (one-tailed) or non-directional (two-tailed). If it is directional, tell whether if it is left-tailed or right tailed. 

a.) A teacher wants to know if listening to popular music affects the performance of pupils. A class of 50 grade 1 pupils was used in the experiment. The mean score was 82 and the standard deviation is 5. A previous study revealed that µ = 81 and the standard deviation = 10.  

b.) A farmer believes that using organic fertilizers on his plants will yield greater income. His average income from the past was P300, 000.00 per year.  

c.) The owner of a factory that sells a particular plastic bottled shampoo claims that the average capacity of a bottle of their product is 200 ml.  

Answer 1

a)

$H_0:\mu=81$ Based on the previous study, the null hypothesis is that the mean score is equal to 81.

$H_a:\mu\ne81$ The aim of the study was to test the effect of listening to popular music on performance. Effect can be positive or negative. Thus, the alternative hypothesis is that the average score is not equal to 81.

The test is non directional (two tailed).

b)

The null hypothesis states that average income will be less than or equal to P300, 000.00 per year with using organic fertilizers on his plants.

The alternative hypothesis states that average income will be greater than P300, 000.00 per year with using organic fertilizers on his plants.

$H_0: \mu\leq300000.00$

$H_1: \mu>300000.00$

This corresponds to a right-tailed (directional , one-tailed) test.

c)

Hypothesis: 

$H_0:\mu=200$

$H_1:\mu\:\not=$ $200$

This is a non directional (two-tailed) test