Company X is known to release some employees and hire new ones every year without changing the total number of employees in the company. A statistical analysis was done, and the following was observed: in year 2020, there were 150 male employees who constituted \( 75 \% \) of the total number of employees. In year \( 2021,60 \% \) of the employees were females. What is the change in the number of female employees from year 2020 to 2021 ?

A developer believes that about \( 72 \% \) of homes in a town have a mortgage. A survey is done and she finds that 822 have mortgages while 321 do not. She knows the critical value is -1,81 The null hypothesis direction Blank 1 L for Left, R for Right, 2 for 2-tailed The 3-decimal alpha value Blank 2 The test statistic Blank 3 The p-value Blank 4

A pharmaceutical company needs to know if its new cholesterol drug, Praxor. is effective at lowering cholesterol levels. It believes that people who take Praxor will average a greater decrease in cholesterol level than people taking a placebo. After the experiment is complete, the researchers find that the 36 participants in the treatment group lowered their cholesterol levels by a mean of 20.6 points with a standard deviation of 2.4 points. The 46 participants in the control group lowered their cholesterol levels by a mean of 19.4 points with a standard deviation of 2.1 points. Assume that the population variances are not equal and test the companys claim at the 0.05 level. Let the treatment group be Population 1 and let the control group be Population 2 . step 2 of 3 : Compute the value of the test statistic. Round your answer to three decimal places.

A pharmaceutical company needs to know if its new cholesterol drug, Praxor, is effective at lowering cholesterol levels. It believes that people who take Praxor will average a greater decrease in cholesterol level than people taking a placebo. After the experiment is complete, the researchers find that the 36 participants in the treatment group lowered their cholesterol levels by a mean of 20.6 points with a standard deviation of 2.4 points. The 46 participants in the control group lowered their cholesterol levels by a mean of 19.4 points with a standard deviation of 2.1 points. Assume that the population variances are not equal and test the companys claim at the 0.05 level. Let the treatment group be Population 1 and let the control group be Population 2 . Step 3 of 3 : Draw a conclusion and interpret the decision.

A pharmaceutical company needs to know if its new cholesterol drug. Praxor, is effective at lowering cholesterol levels. It believes that people who take Praxor will average a greater decrease in cholesterol level than people taking a placebo. After the experiment is complete, the researchers find that the 36 participants in the treatment group lowered their cholesterol levels by a mean of 20.6 points with a standard deviation of 2.4 points. The 46 participants in the control group lowered their cholesterol levels by a mean of 19.4 points with a standard deviation of 2.1 points. Assume that the population variances are not equal and test the companys claim at the 0.05 level. Let the treatment group be Population 1 and let the control group be Population 2 . Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below. \[ H_{0}: \mu_{1}=\mu_{2} \] \( H_{a}: \mu_{1} \)

A professor is concerned that the two sections of college algebra that he teaches are not performing at the same level. To test his claim, he looks at the mean exam score for a random sample of students from each of his classes. In Class 1 , the mean exam score for 14 students is 81.1 with a standard deviation of 7.6 . In Class 2 . the mean exam score for 13 students is 77.4 with a standard deviation of 3.9 . Test the professor's claim at the 0.10 level of significance. Assume that both populations are approximately normal and that the population variances are equal. Let Class 1 be Population 1 and let Class 2 be Population 2 . Step 1 of 3 : state the null and alternative hypotheses for the test. Fill in the blank below. \[ H_{0}: \mu_{1}=\mu_{2} \] \( H_{a}: \mu_{1} \)