P-Hat Proportion of Rainy Days

Steps:

2)
Find p-hat(R), the proportion of days on which it rained given that it rained the pervious day.

3)
Find p-hat (NR) the proportion of days on which it rained given that it did not rain the previous day.

4)
Construct confidence intervals for both p-hat(R) and P-Hat(NR) (you can chose level of confidence)
Draw a conclusion as to whether rain on consecutive days is an independent phenomenon.

5)
State your conclusion by saying there is(or is not) enough of a discrepancies to support the claim that rain on consecutive days is a dependent phenomenon

I am attaching #1 which, hopefully, makes it easy for you to provide me assistance.

thanks,

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... previous day is 37.
Then p-hat(NR) = 37/118= 0.3136

4) We can pick up the 95% level of confidence:
Assume that the sample deviation is given by S = Sqrt[(p)(1 - p)]; and e is the 95% margin of error. The z-score z is the value such that P(-z <Z<z) = 0.95, where Z ~ N(0,1). The margin of error is then given by e = z S/Sqrt(n). However, since 0< p-hat<1, the actual confidence interval for p will be [max(0, m/n - e), min(1,m/n+e)]
From the table we ...