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These stats problems are ruining my holiday!?

I have a few stats problems that I could use some help on. Thanks for all the help!

1. p_hat=281/2450=.114694
q=1 - .114694
Z=2.326
Error=Z(sqrt(pq/n))
Error=.014976
p_hat - error < p_hat < p_hat+error
.0997

2. There is sufficient evidence to reject the null hypothesis and accept alternate hypothesis: the mean score of all NBA games during a particular season was less than 106 points per game since the test statistic falls in the critical region and is greater than the set alpha level. (The result is statistically significant.)

3. We want to use a T-Test even though the sample size is greater than 30, but the population standard deviation is not known.
H0: mu0=mu1
H1: mu0 not equal to mu1
Things we Know:
mu0=1000
x_bar=990
Alpha Level=.05
Sx=80
n=40, df=39
t=-.790569
t=x_bar-mu/(Sx/sqrt(n))
Tc=2.02269 (from table with DF=39)
P-Value=.433977
There is not sufficient evidence to reject the null hypothesis since the P-Value is greater than the
set alpha level of .05 and the test statistic does not fall in the critical region.

4. P=.700, p_hat=.612, alpha=.10, n=50
h0: p≥0.700
h1: p notequal to .700
σ = sqrt[ P * ( 1 - P ) / n ] = = sqrt[ 0.612 * ( 1 - 0.612 ) / 50 ] = .064807
z = (p_hat - P) / σ = (.612 - .70)/.064807 = -1.35787
P-Value: 2(.087253)=.174506

P-Value> Set alpha level of .10, so there is not sufficient evidence to reject the null hypothesis. The result is not statistically significant

Man that was a lot of work. You should split up the questions next time since most people won't respond to 4 questions.

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