can someone help me with this question

the proportion of individuals responding to the standard treatment for a childhood blood disorder has been constant over a number of years, at 64%. A new treatment is being trialled and early results show that of the 125 patients exposed to the new treatment, 87 have responded.

a) can we claim a new improved treatment? conduct an appropriate hypothesis test at a 5% significance level using a critical value approach.

b) what is the P-Value for the test in part a)?

c) if we wanted to be 90% sure that our sample proportion was within 0.05 of the true response rate for the new treatment, how many randomly-selected patients would we need to treat?


thank you for your help

vs.



The test stat is

use a z table since we will approximate this via the central limit theorem

so out of that equation i got the rest stat to be 0.978 and the P-Value 0.8340. is that correct?
therefore the P-Value would be large?

The p-value is because of the alternative hypothesis.

A road is constructed so that the right-turn lane at an intersection has a capacity of 3 cars. Suppose that 30% of cars approaching the intersection want to turn right, and they do so independently.

a) if 15 cars approach the intersection, what is the probability that the right-turn lane will not hold all the cars wanting to turn right?

b) over a week 1428 cars used the intersection
i) what is the distribution of the sample proportion of cars turning right at this intersection, in random samples of this size?

ii) what is the probability that, in such a sample, the proportion turning right is between 0.28 and 0.32?

help meeeeee

Anyone?

is a) binomial (n=15, p=3/10)
P(X>3)=.2969 or is there more to it then this?

b) i) Binomial (n=1428, p=3/10)
is there more to this?

and what would you answer for b) ii) b?