Hypothesis testing help

[ReubenGidlow]

i have this hypothesis testing question: ive done the first half but not sure on what to do for the second (iii) and (iv)

1) sweets called "scruffies" are sold in packs of 18
they come in a variety of colours, and market research shows red is the most populat. they are packed randomly and on average 25% are red

(i) find p of no more than 6 red
X-B(18,0.25)
p(X≤6) = 0.86101...

(ii) find p of exactly 4
p(X=4) = 0.21298...

(iii) 1 in 10 contain 19 sweets instead of 18. what is the p of exactly 4 now
X-B()

(iv) to inscrease sales manufacturer sais increase production of red. (assume contail 18 per pack). pack contains 8 scruffies. test at the 5% significance level if this supports the claim

h0= p=0.25
h1= p≠ 0.25
assume h0 to be true, X-B(18,0.25)


This is where i have got up to on the question and stick on (iii) and (iv). help would be great in the right direction for these

 

[HallsofIvy]

i have this hypothesis testing question: ive done the first half but not sure on what to do for the second (iii) and (iv)

1) sweets called "scruffies" are sold in packs of 18
they come in a variety of colours, and market research shows red is the most populat. they are packed randomly and on average 25% are red

(i) find p of no more than 6 red
X-B(18,0.25)

What does "X" mean? What does "B(18,0.25)" mean?

p(X≤6) = 0.86101...

(ii) find p of exactly 4

"Exactly 4" what? I presume you mean "exactly 4 red" but that should be said.

p(X=4) = 0.21298...

Yes, that is correct.

(iii) 1 in 10 contain 19 sweets instead of 18. what is the p of exactly 4 now
X-B()

Imagine 1000 boxes. 1000 of them contain 19 sweets. How many of them contain exactly 4 red? 9000 of them contain 18 sweets. How many of them contain exactly 4 red? So how many altogether contain exactly 4 red? Divide that by 10000.

(iv) to inscrease sales manufacturer sais increase production of red. (assume contail 18 per pack). pack contains 8 scruffies. test at the 5% significance level if this supports the claim.

Supports what claim? You say "contain 18 per pack" and then immediately say "pack contains 8 scruffies". ????

h0= p=0.25
h1= p≠ 0.25
assume h0 to be true, X-B(18,0.25)


This is where i have got up to on the question and stick on (iii) and (iv). help would be great in the right direction for these