confusing hypothesis testing question help ASAP. Watch

maryamk0002
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the probability that a certain type of seed germinates is estimated to be 0.75. A new batch of seeds is produced which appear to have a lower probability. To check this, a sample of 16 seeds is tested and 8 germinate. Is this evidence, at a 5% significance level of a reduction in the probability?
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Kallisto
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What is given:

sample s = 16
propability p = 0,75 = 75%
a = 5%

The question you must ask yourself is, what is H0 and H1 and is this hypothesis on the right or left side?
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maryamk0002
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Thanks so far I understand H0=0.75 H1<0.75
But I don't understand how to tell if it is on the left or right?
Is it 1 tail and the p-value = 0.02713 which is < 0.05
so there is enough evidence to reject the null hypothesis
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Kallisto
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(Original post by maryamk0002)
Thanks so far I understand H0=0.75 H1<0.75
But I don't understand how to tell if it is on the left or right?
Is it 1 tail and the p-value = 0.02713 which is < 0.05
so there is enough evidence to reject the null hypothesis
To get left or right side for your hypothesis out, ask your the question when you are in accepted and when in rejection region.

Is your hypothesis on the left side, it means that your accepted region is on the right side (rejection region left)

-> the greater the value, the more it is agreed.

Is your hypothesis on the right side, it means that your accepted region is on the left side (rejection region right).

-> the smaller the value, the more it is agreed.

For right side, it is: H0 <= p and H1 > p

For the left side, it is: H0 => p and H1 < p

To find the critical value k for left side, it is:

P(x <= k) <= a

To find the critical value k for right side, it is:

1 - a <= (x <= k - 1)

x = 8 is the value to check.

If your hypothesis is left side, it must be x => k to accept H0, otherwise H1 is true.

If your hypothesis is right side, it must be x <= k to accept H0, otherwise H1 is true.

So can you see whether it is left or right side now?

Note:
=> : 'greater or equal to'
<= : 'smaller or equal to'
Last edited by Kallisto; 1 week ago
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the bear
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it is a single tailed test with

H1: p < 0.75

which means you compare P( X ≤ 8 ) when n = 16 and p = 0.75 to the significance level which is 5%

if P( X ≤ 8 ) is less than 5% you are in the critical region and must reject H0
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