A-level stats

Watch this thread
issy_shep
Badges: 6
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#1
Report Thread starter 5 months ago
#1
Hypothesis tests:
I don't know if I am just overcomplicating this, but can someone help me?
The random variable X has a binomial distribution with n=50. the value of the binomial probability, p, is unknown. Carly decides to do a hypothesis test at 5% significance level to investigate whether the value of p is less than 0.4.
a. state H0 & H1
b. explain what a 5% significance level means
c. p(x <= 14) assuming p = 0.4
d. explain whether your answer to part c is statistically significant.
e. identify critical region & acceptance region for the hypothesis test.
f. explain 'test statistic' & identify test statistic in the hypothesis test.
My answers so far:
a. no idea, maybe: H0: p < 0.4 H1: p >0.4
b. how much 'evidence' is required to reject H0 in favour of H1.
c. 0.054
d. 0.054 > 0.05 - not statistically significant as there isn't enough evidence to reject H0 in favour of H1
e. CR: X <= 12 and X >= 28 ; AR: X >= 13 and x <= 27
f. no idea
Thankyou!!
0
reply
old_engineer
Badges: 11
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#2
Report 5 months ago
#2
(Original post by issy_shep)
Hypothesis tests:
I don't know if I am just overcomplicating this, but can someone help me?
The random variable X has a binomial distribution with n=50. the value of the binomial probability, p, is unknown. Carly decides to do a hypothesis test at 5% significance level to investigate whether the value of p is less than 0.4.
a. state H0 & H1
b. explain what a 5% significance level means
c. p(x <= 14) assuming p = 0.4
d. explain whether your answer to part c is statistically significant.
e. identify critical region & acceptance region for the hypothesis test.
f. explain 'test statistic' & identify test statistic in the hypothesis test.
My answers so far:
a. no idea, maybe: H0: p < 0.4 H1: p >0.4
b. how much 'evidence' is required to reject H0 in favour of H1.
c. 0.054
d. 0.054 > 0.05 - not statistically significant as there isn't enough evidence to reject H0 in favour of H1
e. CR: X <= 12 and X >= 28 ; AR: X >= 13 and x <= 27
f. no idea
Thankyou!!
I'm uneasy about this question, as hypothesis tests are usually conducted to test whether a well established population parameter has changed, based on the result of a sample test. Here, the question starts by saying that p is unknown, but I think the implication is that you're supposed to assume that p = 0.4 and then to check whether or not a test result in the range X <= 14 is significant at the 5% level of significance (i.e. that the test result provides evidence that p < 0.4). If I'm right in my assumptions about what the question is asking, your H0 should be p = 0.4. Note also that we are looking at a one-tailed test here, as we're testing for evidence that p < 0.4, not that p <> 4. (Using <> to denote not equal). Based on those thoughts, would you like to have another go?
0
reply
bexxr
Badges: 7
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#3
Report 5 months ago
#3
As old_engineer states, H0: p = 0.4 and H1: p < 0.4

A hypothesis is a claim or a statement that might or might not be true.
A hypothesis test is a method of testing a hypothesis about a population using observed data from a sample.
You need 2 hypotheses for every hypothesis test - a null hypothesis (H0) and an alternative hypothesis (H1).

The null hypothesis (H0) is a statement about the value of a population parameter, so in this case ... H0: p = 0.4

The alternative hypothesis (H1) is what you're going to conclude if you end up rejecting H0.
There are two kinds of alternative hypothesis:
- one tailed (specifying whether the parameter you're investigating is greater than or less than the value you used in H0).
- two tailed (doesn't specify whether the parameter you're investigating is greater or less than the value you used in H0).

Therefore, as the question states that Carly is investigating whether the value of p is less than 0.4, then H1: p < 0.4. So this is a one tailed test.

The significance level of a test determines how unlikely your data needs to be under the the null hypothesis (H0) before you reject H0.
For a significance level of 5%, this would mean that you would only reject H0 if your observed data fell into the most extreme 5% of possible outcomes.
So the significance level of 5% means that there is a probability of 0.05 of rejecting H0 when H0 is true.

Your answer to part c) is correct: P(X<=14) = 0.0540

You answer to part d) is also correct.

Part e) is incorrect.
0
reply
bexxr
Badges: 7
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#4
Report 5 months ago
#4
Part e)

The critical region (CR) is the set of all values of the test statistic that would cause you to reject H0.

Remember that you are carrying out a one-tailed test, so we're only looking at the low end of the distribution (because H1 was of the form H1: p<0.4). Therefore, your CR and AR will be one set of values, not two as you have calculated (two sets would be for a two-tailed test).

To find the critical region, you need to use the binomial tables to find the two values of x for which P(X≤x) is either side of the significance level 0.05
Last edited by bexxr; 5 months ago
0
reply
old_engineer
Badges: 11
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#5
Report 5 months ago
#5
(Original post by bexxr)
Part e)

The critical region (CR) is the set of all values of the test statistic that would cause you to reject H0.

...deleted...
Not sure whether you've seen the posting guidelines (sticky): hints not full solutions.
1
reply
bexxr
Badges: 7
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#6
Report 5 months ago
#6
(Original post by old_engineer)
Not sure whether you've seen the posting guidelines (sticky): hints not full solutions.
Thank you! I've amended the post
0
reply
issy_shep
Badges: 6
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#7
Report Thread starter 5 months ago
#7
(Original post by bexxr)
Part e)

The critical region (CR) is the set of all values of the test statistic that would cause you to reject H0.

Remember that you are carrying out a one-tailed test, so we're only looking at the low end of the distribution (because H1 was of the form H1: p<0.4). Therefore, your CR and AR will be one set of values, not two as you have calculated (two sets would be for a two-tailed test).

To find the critical region, you need to use the binomial tables to find the two values of x for which P(X≤x) is either side of the significance level 0.05
what does acceptance region mean? how would i work it out?
0
reply
bexxr
Badges: 7
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#8
Report 5 months ago
#8
(Original post by issy_shep)
what does acceptance region mean? how would i work it out?
The acceptance region is the set of all values of the test statistic that would cause you to fail to reject H0 (remember, we don't say "accept" but "fail to reject").

For example, if the critical region is X≤8 then the acceptance region would be X≥9 (FYI this is just an example and NOT the answer to part e)
0
reply
issy_shep
Badges: 6
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#9
Report Thread starter 5 months ago
#9
(Original post by bexxr)
The acceptance region is the set of all values of the test statistic that would cause you to fail to reject H0 (remember, we don't say "accept" but "fail to reject").

For example, if the critical region is X≤8 then the acceptance region would be X≥9 (FYI this is just an example and NOT the answer to part e)
Okay ty, and what about test statistic?
0
reply
bexxr
Badges: 7
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#10
Report 5 months ago
#10
(Original post by issy_shep)
Okay ty, and what about test statistic?
I don't mean to sound rude, but if you don't know what the test statistic is, I suggest you re-learn this chapter of statistics as you clearly don't understand it. Hypothesis testing always comes up in the A level exam, so it is really worth your while to study and understand it properly. Check out TLMaths here: https://sites.google.com/view/tlmath...thesis-testing Start at the beginning (O1) and work through the videos in order.
0
reply
issy_shep
Badges: 6
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#11
Report Thread starter 5 months ago
#11
(Original post by bexxr)
I don't mean to sound rude, but if you don't know what the test statistic is, I suggest you re-learn this chapter of statistics as you clearly don't understand it. Hypothesis testing always comes up in the A level exam, so it is really worth your while to study and understand it properly. Check out TLMaths here: https://sites.google.com/view/tlmath...thesis-testing Start at the beginning (O1) and work through the videos in order.
I had covid a week before we broke up for Xmas which was at the time when they taught it in class so I haven't seen the teacher yet. I have tried to self teach myself it all & I will find the teacher when I go back to sixth form. Test statistic didn't come up in the work he set. I have turned to TSR as it is generally a good place to ask questions & most people are generally very helpful, sometimes more helpful than Google or a textbook.
0
reply
bexxr
Badges: 7
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#12
Report 5 months ago
#12
(Original post by issy_shep)
I had covid a week before we broke up for Xmas which was at the time when they taught it in class so I haven't seen the teacher yet. I have tried to self teach myself it all & I will find the teacher when I go back to sixth form. Test statistic didn't come up in the work he set. I have turned to TSR as it is generally a good place to ask questions & most people are generally very helpful, sometimes more helpful than Google or a textbook.
I'm really sorry to hear you have been ill. The most helpful thing I can suggest is to watch the TLMaths video lessons that I linked above - they really helped me understand statistics
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest

Were exams easier or harder than you expected?

Easier (36)
26.87%
As I expected (44)
32.84%
Harder (47)
35.07%
Something else (tell us in the thread) (7)
5.22%

Watched Threads

View All