Question

I do not know how to answer part b. Can you show me how to conduct a hypothesis test for this problem? As I know the answer for part a is 0.4

Let X be the weight of flour (in g) contained in a 1kg bag of flour made by a certain company and assume X~U(980,1030).

a) What is the probability that the bag of flour has less than 1kg of flour in it?

b) The owner of this factory feels that the probability of a bag of flour weighing less than 1kg is too high, and adjusts the flour dispensing machine to try and reduce this probability. She randomly selects 15 bags of flour from the next day's production and 3 of them are found to weigh less than 1kg. Conduct a hypothesis test to decide if there is enough evidence that she has reduced the probability of a bag of flour containing less than 1kg.

Answer 1

a) Answer = 0.4

Thus, P( bag of flour has less than 1kg of flour ) = 0.4

Let p = P( bag of flour has less than 1kg of flour ) = 0.4

b)

n = 15    ............. Sample of 15 bags

p = 0.4         ..............Population proportion of bags weighing less than 1 kg

3 out of 15 sample bags weigh less than 1 kg

To test the hypothesis that she has reduced the probability of a bag of flour containing less than 1kg.

The null and alternative hypotheses are

Ho : p = 0.4

Ha : p < 0.4

We find z, the test statistic as
where

z = -1.5811

We find p-value using Standard Normal tables or Excel function NORM.S.DIST                  
p-value = NORM.S.DIST(-1.5811, TRUE)                   (for left tailed we keep the second parameter TRUE)
p-value = 0.0569                 

Let α = 0.05              which is the significance level                  
0.0569 > 0.05                  
That is p-value < α                  
Hence, we Do not reject Ho                  
Conclusion :                  
There does not exist sufficient evidence to conclude that she has reduced the probability of a bag of flour containing less than 1kg         

That is ,

She has not reduced the probability of a bag of flour containing less than 1kg.