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Solve the problem. Find the critical value (χ²ₐ) corresponding to a sample size of 19 and a confidence level of 99 per

a. Use the chi-square table to find the critical value.
b. Use the standard normal distribution table to find the critical value.
c. Use the t-distribution table to find the critical value.
d. Use the F-distribution table to find the critical value.

User Somy
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1 Answer

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Final answer:

To find the critical value for a sample size of 19 and a 99% confidence level, one would typically use a chi-square table or a t-distribution table for 18 degrees of freedom. A standard normal distribution or F-distribution table would not be appropriate for this context.

Step-by-step explanation:

To find the critical value corresponding to a sample size of 19 and a 99% confidence level, we will use different statistical tables depending on the context. Since the degrees of freedom (df) for the sample size of 19 are 18 (df = n - 1), the critical values can be found as follows:

  • Chi-square distribution: Look up the chi-square value in a chi-square table for 18 degrees of freedom at the 99% level.
  • Standard normal distribution: The standard normal table is used for a z-distribution, which is not appropriate in this context as we are dealing with a small sample size.
  • t-distribution: Consult a t-distribution table using 18 degrees of freedom to find the critical t-value for a 99% confidence level.
  • F-distribution: The F-distribution table is used when comparing two variances, which is not the context of this question.

Looking at reference information, we find that a t-value can be obtained from a table or a calculator. For a t-distribution with 18 degrees of freedom and a 99% confidence level, the critical t-value will be higher than for a 95% confidence level, which was 2.093 for 19 degrees of freedom. It is important to note that a t-distribution is used when the population standard deviation is unknown, which seems to be the case here.

User Frank Guo
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