- #1
mathmari
Gold Member
MHB
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Hey!
A vegetable trader sells potatoes in 5 kg bags. Since potatoes differ in size, it is difficult to ensure that in each bag are exactly 5 kg. The dealer claims that the average weight of the potatoes was 5 kilograms. This has to be checked with a sample.
The sample (n = 25) gives an average value of 5.2 kg and an empirical standard deviation of 0.5 kg. By that sample can we say that that the average weight of the potatoes in the bag differs from 5 kg? The significance level is 0.05.We have the following:
Null hypothesis ($H_0$): The average weight of the potatoes is 5 kg.
Alternative hypothesis ($H_1$): The average weight of the potatoes is not 5 kg, but 5.2kg.
Is this correct? (Wondering)
The Beta error is the possibility that the null hypothesis is hold although it is false.
Then it s asked the following:
How big is the Beta error?
a) 0,25
b) 0,05
c) 0,95
d) 0,1
e) cannot be given I have done the following:
We have that the significance level is 0.05.
So, $P(Z < z) = 0.05$ and we get a z-value of $-1.645$.
We convert this to an X-value: $5-1.645\frac{0.5}{\sqrt{25}}=5-1.645\cdot 0.1=4.8355$
Then we have the follwoing: $P(X > 4.8355) = P\left [z > \frac{3.069-5.2}{0.1}\right ] = P(z > -3.645)=1-P(x\leq -3.645$ , now from a Normal table we get $beta = 1-P(x\leq -3.645 = 1-0.00014=0.99986$.
I must have done something wrong, since this answer is not one of the choices. Bur what? (Wondering)
A vegetable trader sells potatoes in 5 kg bags. Since potatoes differ in size, it is difficult to ensure that in each bag are exactly 5 kg. The dealer claims that the average weight of the potatoes was 5 kilograms. This has to be checked with a sample.
The sample (n = 25) gives an average value of 5.2 kg and an empirical standard deviation of 0.5 kg. By that sample can we say that that the average weight of the potatoes in the bag differs from 5 kg? The significance level is 0.05.We have the following:
Null hypothesis ($H_0$): The average weight of the potatoes is 5 kg.
Alternative hypothesis ($H_1$): The average weight of the potatoes is not 5 kg, but 5.2kg.
Is this correct? (Wondering)
The Beta error is the possibility that the null hypothesis is hold although it is false.
Then it s asked the following:
How big is the Beta error?
a) 0,25
b) 0,05
c) 0,95
d) 0,1
e) cannot be given I have done the following:
We have that the significance level is 0.05.
So, $P(Z < z) = 0.05$ and we get a z-value of $-1.645$.
We convert this to an X-value: $5-1.645\frac{0.5}{\sqrt{25}}=5-1.645\cdot 0.1=4.8355$
Then we have the follwoing: $P(X > 4.8355) = P\left [z > \frac{3.069-5.2}{0.1}\right ] = P(z > -3.645)=1-P(x\leq -3.645$ , now from a Normal table we get $beta = 1-P(x\leq -3.645 = 1-0.00014=0.99986$.
I must have done something wrong, since this answer is not one of the choices. Bur what? (Wondering)