Question

California had stricter gun laws than Texas. However, California had a greater proportion of gun murders than Texas. Here we test whether or not the proportion was significantly greater in California. A significant difference is one that is unlikely to be a result of random variation. The table summarizes the data for each state. The p̂'s are actually population proportions but you should treat them as sample proportions. The standard error (SE) is given to save calculation time if you are not using software.

Data Summary

	number of	total number	Proportion
State	gun murders (x)	of murders (n)	p̂
California	1220	1788	0.68233
Texas	699	1086	0.64365

SE = 0.01812

The Test: Test the claim that the proportion of gun murders was significantly greater in California than Texas in 2011. Use a 0.01 significance level.

(a) Letting p̂₁ be the proportion of gun murders in California and p̂₂ be the proportion from Texas, calculate the test statistic using software or the formula

z =

(p̂₁ − p̂₂) − δ_p

SE

where δ_p is the hypothesized difference in proportions from the null hypothesis and the standard error (SE) is given with the data. Round your answer to 2 decimal places.
z =  
To account for hand calculations -vs- software, your answer must be within 0.01 of the true answer.

(b) Use software or the z-table to get the P-value of the test statistic. Round to 4 decimal places.
P-value =  

(c) What is the conclusion regarding the null hypothesis?

reject H₀

fail to reject H₀    

(d) Choose the appropriate concluding statement.

The data supports the claim that the proportion of gun murders was significantly greater in California than Texas.

While the proportion of gun murders in California was greater than Texas, the difference was not great enough to be considered significant.     

We have proven that the stricter gun laws in California actually increased the proportion of gun murders above the rate in Texas.

We have proven there was no difference in the proportion of gun murders between California and Texas.

Answer 1

To test against

Given,

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at 5% level of significance if P-value < 0.01

Now,

The value of the test statistic

and p-value =

c) Since p-value > 0.01, so we fail to reject H₀ at 5% level of significance.

d) Conclusion : While the proportion of gun murders in California was greater than Texas, the difference was not great enough to be considered significant.