Question

Members of the city council want to know if a majority of city residents supports a $1\%$increase in the sales tax to fund road repairs. To investigate, they survey a random sample of $300$city residents and use the results to test the following hypotheses:

$H_0:p=0.50$

$H_a:p>0.50$

where $p$is the proportion of all city residents who support a 1% increase in the sales tax to fund road repairs.

A Type I error in the context of this study occurs if the city council

a. finds convincing evidence that a majority of residents supports the tax increase, when in reality there isn’t convincing evidence that a majority supports the increase.

b. finds convincing evidence that a majority of residents supports the tax increase, when in reality at most $50\%$of city residents support the increase.

c. finds convincing evidence that a majority of residents supports the tax increase, when in reality more than $50\%$of city residents do support the increase.

d. does not find convincing evidence that a majority of residents supports the tax increase, when in reality more than $50\%$of city residents do support the increase.

Short answer

Option (a) is correct.

Step-by-step solution

Given Information

It is given that $H_0:p=0.50$

$H_1:p>0.50$

Explanation

Once null hypothesis $H_0$is true, type I error will reject it.

If this is the case, then there will be enough proof that alternate hypothesis is true.

It mean that there is enough convincing proof that residents who keep the tax increase is $0.50$and hence convincing proof is present that majority residents help in tax increase.

$H_0$is true if all city residents who help in increase of tax is $0.50$. So, once there is not convincing proof that bulk catalysis the increase.