There are 100 freshman students at a school. The probability that a freshman plays a sport is 0.55. The probability that a fresh

Answer:

A Type I error could occur if the test shows that the proportion is above 90%, while in reality, the actual proportion is 90%.

Step-by-step explanation:

Machines in a factory produce circular washers that meet a specific diameter.

The quality control manager routinely assesses samples of washers to ensure that more than 90% conform to the specified diameter.

Let p represent the proportion of washers that meet the specified diameter

Thus, Null hypothesis: p = 90%

Alternative Hypothesis: p > 90%

Here, the null hypothesis posits that the proportion is exactly 90%. In contrast, the alternative hypothesis suggests that the proportion exceeds 90%.

Now, a Type I error indicates the probability of rejecting the null hypothesis while it is actually true or, in simple terms, the likelihood of incorrectly rejecting a valid hypothesis.

Thus, based on our question, a Type I error would declare that the test convincingly indicates the proportion is over 90%, while in truth, it remains 90%.

Answer: OPTION B

Step-by-step explanation:

The red graph depicts the fundamental form of a quadratic function (the most basic version), with its vertex located at the origin.

The function g(x) results from moving the parent function 2 units to the right and 1 unit upwards.

As a consequence, considering this, the transformation takes the following structure:

The horizontal displacement is dictated by the value of h, while the vertical shift is determined by k.

<pThus, the resulting function is:

(x1,x2), (y1,y2)

(1,3), (5,0)

0-3/5-1

-3/4

Response:

(a) 3, 5, and 6

Detailed explanation:

In this study, 43 participants will be treated with a gel containing tooth-whitening agents, while the remaining 42 will receive a placebo. Consequently, a placebo is in use.

The selection process for the 43 individuals receiving the gel will be random.

Post-experiment, the whiteness levels of both groups will be compared to analyze the gel's effect.

For true randomness in the experiment, options 3, 5, and 6 are applicable.

(b)

In order for the experiment to be double-blind, the evaluators analyzing the whiteness, as well as the participants, must not know which individuals were given the whitening gel versus the placebo.

The simplified expression is 10m + 20.5, where m stands for the total number of months. Initially, we can express her expenses as follows: 8.5 + 62.5m and 12 + 3.75m. Adding these two expressions together yields a combined equation of: 10m + 20.5.