Question 1042154
The sample proportion is 0.55
Ho: There is no majority who support gun control, or p< = 0.50
Ha: There is a majority, p>0.50.
alpha=0.05, and the sample was randomly chosen among the population.
Test statistic is a z-test for 1 sample proportion, with critical value of z>1.645
z=(p obs-p hypoth)/sqrt((p)(1-p)/n))
z=(0.55-0.50)/sqrt(0.55)*0.45)/600)
=0.05/0.0203
z=2.46
p-value is 0.007

This is in the rejection region.
The null hypothesis is rejected and the conclusion is that a majority support gun control.
90% CI has an interval of z(0.90)*Std error.
That is 1.645*0.0203=0.0333
The interval is around 0.55
(0.517,0.583)
every value in that interval could be consistent, and 0.50 is not in the interval, so the above is confirmed.
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This is a simple random sample.
5|47
6|5545006.52.534023.5045
7|213101
Mean is 64.86 inches
sd=5.088 inches
df=24
t 0.90,df=24=1.711,
standard error is s/sqrt(n)=5.088/5=1.018
90% CI is mean +/- t from above* SE
t*SE=1.711*1.018=1.74
The interval is 64.86+/-1.74, or (63.12,66.60)
That means that we are 90% confident that the true mean, which we do not know, lies in the above interval.