Answer:
We conclude that the rate of inaccurate orders is greater than 10%.
Step-by-step explanation:
We are given that in a study of the accuracy of fast food drive-through orders, one restaurant had 40 orders that were not accurate among 307 orders observed.
Let p = <u><em>population proportion rate of inaccurate orders</em></u>
So, Null Hypothesis, : p
10% {means that the rate of inaccurate orders is less than or equal to 10%}
Alternate Hypothesis, : p > 10% {means that the rate of inaccurate orders is greater than 10%}
The test statistics that will be used here is <u>One-sample z-test</u> for proportions;
T.S. = ~ N(0,1)
where, = sample proportion of inaccurate orders =
= 0.13
n = sample of orders = 307
So,<u><em> the test statistics</em></u> =
= 1.75
The value of z-test statistics is 1.75.
<u>Also, the P-value of the test statistics is given by;</u>
P-value = P(Z > 1.75) = 1 - P(Z 1.75)
= 1 - 0.95994 = <u>0.04006</u>
Now, at 0.05 level of significance, the z table gives a critical value of 1.645 for the right-tailed test.
Since the value of our test statistics is more than the critical value of z as 1.75 > 1.645, so <u><em>we have sufficient evidence to reject our null hypothesis</em></u> as it will fall in the rejection region.
Therefore, we conclude that the rate of inaccurate orders is greater than 10%.