The Next Questions Are Based On The Following Information:
The manufacturer of a new chewing gum claims that at least 80% of dentists surveyed prefer their type of gum and recommend it for their patients who chew gum.An independent consumer research firm decides to test their claim.The findings in a sample of 200 dentists indicate that 74.1% of the respondents do actually prefer their gum.
-The value of the test statistic is:
A)2.086
B)1.444
C)-2.086
D)-1.444

Question

Quizplus · Accepted Answer

The test statistic is calculated using the formula for a proportion test statistic: $z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$, where $\hat{p}$ is the sample proportion, $p_0$ is the hypothesized population proportion, and $n$ is the sample size. Here, $\hat{p} = 0.741$, $p_0 = 0.80$, and $n = 200$. Plugging these values into the formula gives a negative z-value, indicating that the sample proportion is less than the hypothesized proportion. The correct calculation results in $z = -2.086$, which means the test statistic is -2.086.

The Next Questions Are Based on the Following Information