Question

Math

Posted 5 months ago

```
Francisco was testing $H_{0}: \mu=10$ versus $H_{\mathrm{a}}: \mu>10$ with a sample of 6 observations. His test statistic was $t=1.952$. Assume that the conditions for inference were met.
What is the approximate P-value for Francisco's test?
Choose 1 answer:
(A) $0.10<$ P-value $<0.15$
(B) $0.05<$ P-value $<0.10$
(C) $0.01<$ P-value $<0.05$
(D) P-value $<0.01$
```

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Answer from Sia

Posted 5 months ago

Solution by Steps

step 2

Using the t-distribution table or a calculator with statistical functions, we find the area to the right of $t = 1.952$ for 5 degrees of freedom. This area represents the p-value for a one-tailed test

step 3

The p-value is the probability that the t-statistic would be as extreme as, or more extreme than, the observed value under the null hypothesis. Since the alternative hypothesis is $\mu > 10$, we are conducting a right-tailed test

step 4

The p-value corresponding to $t = 1.952$ with 5 degrees of freedom is between 0.05 and 0.10

B

Key Concept

p-value and t-distribution

Explanation

The p-value is found by looking up the t-statistic in a t-distribution table with the appropriate degrees of freedom for a one-tailed test. It represents the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value if the null hypothesis is true.

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