The mentioned exercise concerns a test about the mean contents of cola bottles. The hypotheses are

$$\begin{aligned} & H_0: \mu=300 \\ & H_a: \mu<300 \end{aligned}$$

The sample size is n=6, and the population is assumed to have a normal distribution with $\sigma=3$. A 5% significance test rejects $H_0$ if $z \leq-1.645$, where the test statistic z is

$$z=\frac{\bar{x}-300}{3 / \sqrt{6}}$$

Power calculations help us see how large a shortfall in the bottle contents the test can be expected to detect.

Find the power of this test against the alternative $\mu=299$.

Carta Jose Andres. Escribele una carta al cocinero Jose Andres. Puedes preguntarle acerca de los aceites, las especies y las hierbas que tiene en su casa, sobre el mercado en el que compra los ingredientes, sobre la receta de huevos con el chorizo y con patatas o sobre cualquier otra receta espanola que te interese.

Busca en el diccionario el significado de las siguientes hierbas y aves. Luego, subraya las hierbas y las aves que se mencionan en el video. 1-Hierbas: albahaca, estragon,menta,oregano,perejil,romero, salvia, tomillo. 2-Aves: aguila, avestruz, codorniz, gallina, golondrina, oca, pata

The Degree of Reading Power (DRP) is a test of the reading ability of children. Here are DRP scores for a sample of 44 third-grade students in a suburban school district:

$$\begin{array}{lllllllllll}40 & 26 & 39 & 14 & 42 & 18 & 25 & 43 & 46 & 27 & 19 \\ 47 & 19 & 26 & 35 & 34 & 15 & 44 & 40 & 38 & 31 & 46 \\ 52 & 25 & 35 & 35 & 33 & 29 & 34 & 41 & 49 & 28 & 52 \\ 47 & 35 & 48 & 22 & 33 & 41 & 51 & 27 & 14 & 54 & 45\end{array}$$

Suppose that the standard deviation of the population of DRP scores is known to be $\sigma$=11. Give a 99% confidence interval for the mean score in the school district.

The Degree of Reading Power (DRP) is a test of the reading ability of children. Here are DRP scores for a sample of 44 third-grade students in a suburban school district:

$$\begin{array}{lllllllllll}40 & 26 & 39 & 14 & 42 & 18 & 25 & 43 & 46 & 27 & 19 \\ 47 & 19 & 26 & 35 & 34 & 15 & 44 & 40 & 38 & 31 & 46 \\ 52 & 25 & 35 & 35 & 33 & 29 & 34 & 41 & 49 & 28 & 52 \\ 47 & 35 & 48 & 22 & 33 & 41 & 51 & 27 & 14 & 54 & 45\end{array}$$

We expect the distribution of DRP scores to be close to normal. Make a stemplot or histogram of the distribution of these 44 scores and describe its shape.

The cola maker of the mentioned example determines that a sweetness loss is too large to accept if the mean response for all tasters is $\mu=1.1$. Will a 5% significance test of the hypotheses

$$\begin{aligned} & H_0: \mu=0 \\ & H_d: \mu>0 \end{aligned}$$

based on a sample of 10 tasters usually detect a change this great. We want the power of the test against the alternative $\mu=1.1$. This is the probability that the test rejects $H_0$ when $\mu=1.1$ is true. The calculation method is similar to that for Type II errors.

The power is the probability of this event supposing that the alternative is true. Standardize using $\mu=1.1$ to find the probability that $\bar{x}$ takes a value that leads to rejection of $\mathrm{H}_0$.

Discusion socratica. En grupos pequenos, consten las siguientes preguntas y anadan otras para extender la discusion. 1-¿Por que dice la locutora que esta oferta de turismo es "poco convencional"? 2-¿Como afectaria este tipo de turismo al ser humano y al medio ambiente? 3-¿Que quiere decir la expresion "disfrutar a pleno pulmon de la naturaleza" y por que seria provechoso para las familias? 4-¿Te interesa este tipo de turismo? Explica tu respuesta. 5-Si tuvieras que escoger entre un viaje a Costa Rica para participar en el programa de Carlos Sanchez o un viaje a la Ciudad de Mexico, ¿cual escogerias y por que?

You are thinking about opening a restaurant and are searching for a good location. From the research you have done, you know that the mean income of those living near the restaurant must be over $45,000 to support the type of upscale restaurant you wish to open. You decide to take a simple random sample of 50 people living near one potential location. Based on the mean income of this sample, you will decide whether to open a restaurant there. A number of similar studies have shown that$\sigma$=$ 5,000. If the mean income in a certain area is $ 47,000, how likely are you not to open a restaurant in that area? What is the probability of a Type II error?

The cola maker of the mentioned example determines that a sweetness loss is too large to accept if the mean response for all tasters is $\mu=1.1$. Will a 5% significance test of the hypotheses

$$\begin{aligned} & H_0: \mu=0 \\ & H_d: \mu>0 \end{aligned}$$

based on a sample of 10 tasters usually detect a change this great. We want the power of the test against the alternative $\mu=1.1$. This is the probability that the test rejects $H_0$ when $\mu=1.1$ is true. The calculation method is similar to that for Type II errors.

Write the rule for rejecting $H_0$ in terms of $\bar{x}$. We know that $\sigma=1$, so the test rejects $H_0$ at the $\alpha=0.05$ level when

$$z=\frac{\bar{x}-0}{1 / \sqrt{10}} \geq 1.645$$

Restate this in terms of $\bar{x}$.

You are thinking about opening a restaurant and are searching for a good location. From the research you have done, you know that the mean income of those living near the restaurant must be over $45,000 to support the type of upscale restaurant you wish to open. You decide to take a simple random sample of 50 people living near one potential location. Based on the mean income of this sample, you will decide whether to open a restaurant there. A number of similar studies have shown that$\sigma$=$ 5,000. Based on your choice in the previous part, how high will the sample mean need to be before you decide to open a restaurant in that area?

You are thinking about opening a restaurant and are searching for a good location. From the research you have done, you know that the mean income of those living near the restaurant must be over $45,000 to support the type of upscale restaurant you wish to open. You decide to take a simple random sample of 50 people living near one potential location. Based on the mean income of this sample, you will decide whether to open a restaurant there. A number of similar studies have shown that$\sigma$=$ 5,000. If you had to choose one of the "standard" significance levels for your significance test, would you choose $\alpha$=0.01,0.05, or 0.10? Justify your choice.

You are thinking about opening a restaurant and are searching for a good location. From the research you have done, you know that the mean income of those living near the restaurant must be over $45,000 to support the type of upscale restaurant you wish to open. You decide to take a simple random sample of 50 people living near one potential location. Based on the mean income of this sample, you will decide whether to open a restaurant there. A number of similar studies have shown that$\sigma$=$ 5,000. State the null and alternative hypotheses.

Suppose that you have an SRS of size n=9 from a normal distribution with $\sigma$=1. You wish to test

$$\begin{aligned} & H_0: \mu=0 \\ & H_a: \mu>0 \end{aligned}$$

You decide to reject $H_0$ if $\bar{x}>0$ and to accept $H_0$ otherwise. Find the probability of a Type II error when $\mu=1$

You are thinking about opening a restaurant and are searching for a good location. From research you have done, you know that the mean income of those living near the restaurant must be over $45,000 to support the type of upscale restaurant you wish to open. You decide to take a simple random sample of 50 people living near one potential location. Based on the mean income of this sample, you will decide whether to open a restaurant there. A number of similar studies have shown that$\sigma$=$ 5,000. Which of the two types of error is the most serious? Explain!