Answer
a)Two-tailed.
b)z=1.45.
c)P=0.146.
d)p=0.35, fail to reject null hypothesis
e)There is not sufficient evidence to support that the proportion of homes with a gun is not equal to 0.35.
Work Step by Step
a) The alternative hypothesis is: $p\ne0.35$. If the alternative hypothesis contains $\ne$ then the test is two-tailed. If the alternative hypothesis contains < then the test is left-tailed. If the alternative hypothesis contains > then the test is right-tailed. Hence it is two-tailed.
b) The value of the test statistic is: z=1.45.
c)The value of P is: P=0.146.
d)By using the alternative hypothesis the null hypothesis says: p=0.35. If the P-value is less than $\alpha$, which is the significance level, then this means the rejection of the null hypothesis. Hence:P=0.146 is more than $\alpha=0.05$, hence we fail to reject the null hypothesis.
e)By d) we fail to reject the null hypothesis. Hence we can say that there is not sufficient evidence to support that the proportion of homes with a gun is not equal to 0.35.
