Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can be completed in a mean time of 15 minutes or less. If a longer mean survey time is necessary, premium rate is charged. Suppose a sample of 35 surveys produces the data in the Microsoft Excel Online file below. Use a known \( \sigma=4 \) minutes. Is the premium rate justified? Compute the value of the test statistic (to 2 decimals).

A college student is interested in investigating the daim that students who graduate with a master's degree earn higher salaries, on average, than those who finish with a bachelor's degree. She surveys, at random, 36 recent graduates who completed their master's degrees, and finds that their mean salary is \( \$ 35,000 \) per year. The standard deviation of annual salaries for the population of recent graduates who have master's degrees is known to be \( \$ 3400 \). She also surveys, at random. 48 recent graduates who completed their bachelor's degrees, and finds that their mean salary is \( \$ 34,100 \) per year. The standard deviation of annual salaries for the population of recent graduates with only bachelor's degrees is known to be \( \$ 1100 \). Test the claim at the 0.10 level of significance. Let recent graduates with a master's degree be Population 1 and let recent graduates with a bachelor's degree be Population 2 . Step 3 of 3 : Draw a conclusion and interpret the decision.

Fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 50 randomly selected people who train in groups, and finds that they run a mean of 45.5 miles per week. Assume that the population standard deviation for group runners is known to be 2.6 miles per week. She also interviews a random sample of 47 people who train on their own and finds that they run a mean of 44.4 miles per week. Assume that the population standard deviation for people who run by themselves is 1.1 miles per week. Test the claim at the 0.02 level of significance. Let group runners training for marathons be Population 1 and let individual runners training for marathons be Population 2. Step 3 of 3: Draw a conclusion and interpret the decision.

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?

Fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 50 randomly selected people who train in groups, and finds that they run a mean of 45.5 miles per week. Assume that the population standard deviation for group runners is known to be 2.6 miles per week. She also interviews a random sample of 47 people who train on their own and finds that they run a mean of 44.4 miles per week. Assume that the population standard deviation for people who run by themselves is 1.1 miles per week. Test the claim at the 0.02 level of significance. Let group runners training for marathons be Population 1 and let individual runners training for marathons be Population 2 . Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below. \[ H_{0}: \mu_{1}=\mu_{2} \]

Fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 50 randomly selected people who train in groups, and finds that they run a mean of 45.5 miles per week. Assume that the population standard deviation for group runners is known to be 2.6 miles per week. She also interviews a random sample of 47 people who train on their own and finds that they run a mean of 44.4 miles per week. Assume that the population standard deviation for people who run by themselves is 1.1 miles per week. Test the claim at the 0.02 level of significance. Let group runners training for marathons be Population 1 and let individual runners training for marathons be Population 2 . Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places.