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A quality control manager believes that there are too many defective light bulbs being produced, higherthan the advertised rate. The manager's null hypothesis is that the production line of light bulbs has adefect rate of p = 0.025 (the light bulb's stated defect rate). He does a hypothesis test with a significancelevel of 0.05. Symbolically, the null and alternative hypothesis are as follows: H0: p = 0.025 and Ha: p >0.025. Choose the statement that best describes the significance level in the context of the hypothesistest.A) The significance level of 0.05 is the defect rate we believe is the true defect rate.B) The significance level of 0.05 is the probability of concluding that the defect rate is equal to 0.025 whenin fact it is greater than 0.025.C) The significance level of 0.05 is the probability of concluding that the defect rate is higher than 0.025when in fact the defect rate is equal to 0.025.D) The significance level of 0.05 is the test statistic that we will use to compare the observed outcome tothe null hypothesis.

Question

A quality control manager believes that there are too many defective light bulbs being produced, higherthan the advertised rate. The manager's null hypothesis is that the production line of light bulbs has adefect rate of p = 0.025 (the light bulb's stated defect rate). He does a hypothesis test with a significancelevel of 0.05. Symbolically, the null and alternative hypothesis are as follows: H0: p = 0.025 and Ha: p >0.025. Choose the statement that best describes the significance level in the context of the hypothesistest.A) The significance level of 0.05 is the defect rate we believe is the true defect rate.B) The significance level of 0.05 is the probability of concluding that the defect rate is equal to 0.025 whenin fact it is greater than 0.025.C) The significance level of 0.05 is the probability of concluding that the defect rate is higher than 0.025when in fact the defect rate is equal to 0.025.D) The significance level of 0.05 is the test statistic that we will use to compare the observed outcome tothe null hypothesis.

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Solution

Para responder a la pregunta paso a paso, primero debemos entender qué es el nivel de significancia en el contexto de una prueba de hipótesis.

  1. Definición del nivel de significancia: El nivel de significancia, denotado como α, es la probabilidad de rechazar la hipótesis nula (H0) cuando en realidad es verdadera. En este caso, el nivel de significancia es 0.05.

  2. Interpretación del nivel de significancia: Un nivel de significancia de 0.05 significa que hay un 5% de probabilidad de cometer un error tipo I, es decir, rechazar la hipótesis nula cuando en realidad es verdadera.

  3. Formulación de la hipótesis:

    • Hipótesis nula (H0): p = 0.025 (la tasa de defectos es igual a 0.025).
    • Hipótesis alternativa (Ha): p > 0.025 (la tasa de defectos es mayor a 0.025).
  4. Análisis de las opciones:

    • Opción A: "El nivel de significancia de 0.05 es la tasa de defectos que creemos que es la tasa de defectos verdadera." Esto es incorrecto porque el nivel de significancia no se refiere a la tasa de defectos, sino a la probabilidad de cometer un error tipo I.
    • Opción B: "El nivel de significancia de 0.05 es la probabilidad de concluir que la tasa de defectos es igual a 0.025 cuando de hecho es mayor a 0.025." Esto es incorrecto porque describe un error tipo II, no un error tipo I.
    • Opción C: "El nivel de significancia de 0.05 es la probabilidad de concluir que la tasa de defectos es mayor a 0.025 cuando de hecho la tasa de defectos es igual a 0.025." Esto es correcto porque describe un error tipo I, que es lo que el nivel de significancia representa.
    • Opción D: "El nivel de significancia de 0.05 es la estadística de prueba que usaremos para comparar el resultado observado con la hipótesis nula." Esto es incorrecto porque el nivel de significancia no es la estadística de prueba, sino un umbral para tomar decisiones sobre la hipótesis nula.
  5. Conclusión: La opción que mejor describe el nivel de significancia en el contexto de la prueba de hipótesis es la opción C.

Por lo tanto, la respuesta correcta es: C) El nivel de significancia de 0.05 es la probabilidad de concluir que la tasa de defectos es mayor a 0.025 cuando de hecho la tasa de defectos es igual a 0.025.

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Similar Questions

A quality control manager thinks that there is a higher defective rate on the production line than theadvertised value of p = 0.025. She does a hypothesis test with a significance level of 0.05. Symbolically,the null and alternative hypothesis are as follows: H0: p = 0.025 and Ha: p > 0.025. She calculates ap-value for the hypothesis test of defective light bulbs to be approximately 0.067. Choose the correctinterpretation for the p-value.A) The p-value tells us that the true population rate of defective light bulbs is approximately 0.067.B) The p-value tells us that if the defect rate is 0.025, then the probability that she would observe thepercentage she actually observed or higher is 0.067. At a significance level of 0.05, this would notbe an unusual outcome.C) The p-value tells us that the result is significantly higher than the advertised value using asignificance level of 0.05.D) The p-value tells us that the probability of concluding that the defect rate is equal to 0.025, when infact it is greater than 0.025, is approximately 0.067

The level of significance in hypothesis testing refers to ____________________.*1 pointThe probability of making a wrong decisionThe accuracy of the testThe size of the sampleThe precision of the population parameter

Suppose that a major polling organization wanted to test the hypothesis that there was a change in the president’s “approval rating” since last month. Last month, 35% of the representative sample of registered voters approved of the president. For this month, the null hypothesis was that the approval rating equals 35% and the alternative hypothesis is that the approval rating does not equal 35%. The significance level for this test was 0.05.The results of the hypothesis test of the new survey showed a p-value of 0.008.Which of the following statements is correct? Check all that apply. The results were statistically significant. The results were not statistically significant. The null hypothesis should be rejected. The null hypothesis should be accepted. The null hypothesis cannot be rejected.

Which of the following statements is true regarding the significance level in hypothesis testing?a.It is the probability of a Type 1 errorb.It is the probability of a Type 2 errorc.It is the probability of correctly accepting the null hypothesisd.It is the probability of correctly rejecting the null hypothesisClear my choice

3. Suppose we want to test the null hypothesis H0:p=0.20𝐻0:𝑝=0.20 against the alternative hypothesis Ha:p<0.20𝐻𝑎:𝑝<0.20 . Suppose also that we observed 25 successes in a random sample of 100 subjects and the level of significance is 0.05. What is the observed test statistic for this test?Multiple choice 1 Question 3  z=1.15𝑧=1.15   z=−1.25𝑧=−1.25   z=−1.15𝑧=−1.15   z=1.25

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