Math  /  Data & Statistics

QuestionSuppose a sample size of 87 was used to conduct a right tailed hypothesis test for a single population mean. The null hypothesis was H0:μ=45\mathrm{H}_{0}: \mu=45 and the sample mean was 50 and the p -value was 0.03 . Then there is a 3%3 \% chance that 87 randomly selected individuals from a population with a mean of 45 and the same standard deviation would have a sample mean greater than 50. true false

Studdy Solution

STEP 1

1. The null hypothesis is H0:μ=45\mathrm{H}_{0}: \mu = 45.
2. The sample mean is 50.
3. The p-value is 0.03.
4. The test is right-tailed.
5. The sample size is 87.

STEP 2

1. Understand the meaning of the p-value.
2. Determine if the statement about the p-value is true or false.

STEP 3

The p-value represents the probability of obtaining a sample mean at least as extreme as the observed sample mean (50), assuming the null hypothesis is true (μ=45\mu = 45).

STEP 4

The statement claims there is a 3% chance that 87 randomly selected individuals from a population with a mean of 45 would have a sample mean greater than 50. This is equivalent to the definition of the p-value in a right-tailed test.
The statement is:
true \boxed{\text{true}}

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