4) Existe un medicamento para aliviar la tensión nerviosa, el cual es efectivo en el \( 60 \% \) de los casos. Se han realizado experimentos con un nuevo medicamento en 100 sujetos, que sufren tensión nerviosa y el medicamento ha proporcionado alivio en un \( 70 \% \) de los casos. Con un nivel de significación del \( 5 \% \) ¿es esto suficiente evidencia para concluir que el nuevo medicamento es mejor? ( 2.50 p)

A new small business wants to know if its current radio advertising is effective. The owners decide to look at the mean number of customers who make a purchase in the store on days immediately following days when the radio ads are played as compared to the mean for those days following days when no radio advertisements are played. They found that for 10 days following no advertisements, the mean was 23.6 purchasing customers with a standard deviation of 0.9 customers. On 11 days following advertising, the mean was 24.9 purchasing customers with a standard deviation of 1.5 customers. Test the claim, at the 0.10 level, that the mean number of customers who make a purchase in the store is lower for days following no advertising compared to days following advertising. Assume that both populations are approximately normal and that the population variances are equal. Let days following no advertisements be Population 1 and let days following advertising be Population 2 . Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below. \[ H_{0}: \mu_{1}=\mu_{2} \]

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 19 bottles of regular cola has a mean of 499.2 mL of soda with a standard deviation of 2.6 mL . A random sample of 17 bottles of diet cola has a mean of 501.2 mL of soda with a standard deviation of 3.2 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 3 of 3 : Draw a conclusion and interpret the decision.

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 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 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.