A pharmaceutical company claims that a certain drug causes 80% of people to recover from a disease. Out of 200 people who were given this drug, 153 recovered. For the test of the company’s claim for α = 0.05, do we reject H0 and what is the critical value:

Answer 1

To test the claim of the pharmaceutical company, we will use a hypothesis test.

Null Hypothesis (H0): The drug does not cause 80% of people to recover from the disease.
Alternative Hypothesis (H1): The drug causes 80% of people to recover from the disease.

We will use a significance level (α) of 0.05.

To determine if we reject or fail to reject the null hypothesis, we will use a test statistic and compare it to the critical value.

The test statistic used in this case is the chi-square test statistic. However, since the sample size is greater than 30 and the observations are independent, we can approximate the chi-square distribution with a normal distribution.

First, we calculate the expected number of people who would recover under the assumption that the drug does cause 80% of people to recover.

Expected number of people who would recover = 0.8 * 200 = 160

Now, we can calculate the test statistic:

Test statistic = (Observed - Expected) / sqrt(Expected)
= (153 - 160) / sqrt(160)
≈ -0.438

Next, we compare the test statistic to the critical value.

The critical value is obtained from the standard normal distribution for a two-tailed test and a significance level of 0.05. This critical value corresponds to a z-score of ±1.96.

Since the test statistic (-0.438) is not less than -1.96, and it is not greater than 1.96, we fail to reject the null hypothesis.

Therefore, we do not reject H0, and there is not enough evidence to support the pharmaceutical company's claim that the drug causes 80% of people to recover from the disease.

Note: It's important to note that this analysis assumes that the 200 people were randomly selected and that the sample is representative of the population.

Answer 2

Who was the first to be hung?

Answer 3

The first person to have been hanged is difficult to determine with certainty because capital punishment has been practiced by various civilizations throughout history. Public execution by hanging was one of the common methods used in many societies. However, records and historical documentation of specific individuals who were the first to be hanged are often limited. It is likely that the first person to be hanged predates recorded history.

Answer 4

For the music math problems, fill in the blank with the number that would make the sentence true.

An example is: A half note is shown. + A half note is shown. = A whole rest is shown.

A quarter rest is shown. + ____=A half rest is shown.

Answer 5

A quarter rest is shown. + A quarter rest is shown = A half rest is shown.