En la Encuesta Nacional sobre Disponibilidad y Uso de las Tecnologías de la Información en los Hogares 2020, se afirma que en el \( 44.2 \% \) de los hogares en México se tiene computadora. En una encuesta de 60 hogares ubicados en la zona oriente de la Ciudad de México, se encontró que en 32 de ellas se cuenta con computadora. Al nivel de \( \alpha=0.02 \) ¿Habrá evidencia que indique que el porcentaje de los hogares que cuentan con computadora en la zona oriente de la ciudad es menor que el porcentaje nacional?

A manufacturer fills soda bottles. Periodically the company tests to see if there is a difference between the mean amounts of soda put in bottles of regular cola and diet cola. A random sample of 15 bottles of regular cola has a mean of 500.8 mL of soda with a standard deviation of 2.2 mL . A random sample of 18 bottles of diet cola has a mean of 498.3 mL of soda with a standard deviation of 3.6 mL . Test the claim that there is a difference between the mean fill levels for the two types of soda using a 0.01 level of significance. Assume that both populations are approximately normal and that the population variances are not equal since different machines are used to fill bottles of regular cola and diet cola. Let bottles of regular cola be Population 1 and let bottles of diet cola be Population 2 . Step 1 of \( 3: \) State the null and alternative hypotheses for the test. Fill in the blank below.

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 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. \[ H_{0}: \mu_{1}=\mu_{2} \] \( H_{a}: \mu_{1} \)

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. \[ H_{0}: \mu_{1}=\mu_{2} \] \( H_{a}: \mu_{1} \)