Question

Are seat belts effective at saving lives? We wish to examine whether or not the use of seatbelts reduces fatalities at the alpha=0.10 level of significance. Let Pn represent the proportion of non-seatbelt wearing passengers who were involved in a crash and died and Py represent the proportion of seatbelt wearing passengers who were involved in a crash and died. (Round result to three decimal places)

Note: The data used in this study were obtained through observational study...no experiment was conducted

Which would be correct hypotheses for this test?

H0: Pn = Py, H1: Pn > Py

H0: Pn = Py, H1: Pn < Py

H0: Pn ≠ Py, H1: Pn > Py

H0: Pn = Py, H1: Pn ≠ Py

In a random sample of 482 non-seatbelt wearing passengers involved in a car crash, 43 were killed. In a random sample of 468 seatbelt wearing passengers involved in a car crash, 20 were killed. Find the test statistic:

___________

Give the P-value

____________

Which is the correct result:

Reject the Null Hypothesis

Do not Reject the Null Hypothesis

Which would be the appropriate conclusion?

There is not significant evidence to suggest that seatbelts are effective in reducing fatalities

There is significant evidence to suggest that seatbelts are effective in reducing fatalities

Answer 1

we want to check whether or not the use of seatbelts reduces fatalities,, so its a left tailed hypothesis, i.e. we want to test whether or not Pn is less than Py

So, Null hypothesis

Alternate hypothesis

option A is correct.

We have Pn = (43/482) = 0.089 and Py =20/468 = 0.043

P =

where x1 =43, x2 = 20, n1 = 482 and n2 =468

we get, P= (43+20)/(482+468) = 63/950 = 0.066

Z statistic calculation

z =

settig the given values, we get

z =

this gives us

z = 2.856 (rounded to three decimals) or 2.86 (rounded to 2 decimals)

Now, we have to find the value of

using the identity

so, we can write it as

So, the required p value is 0.0021 (rounded to 4 decimals)

Reject the null hypothesis, as the p value is significant at 0.05 level of significance because p value is less than 0.05.

We can conclude that the seatbelts reduces the number of fatalities significantly

So, option B is correct. "There is significant evidence to suggest that seatbelts are effective in reducing fatalities"