You wish to test the following claim (Ha) at a significance level of α=0.001. Ho:μ=69.1
Ha:μ<69.1 You believe the population is normally distributed and you know the standard deviation is σ=8.8. You obtain a sample mean of ¯x=67 for a sample of size n=69
. What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value = The p-value is...
less than (or equal to) α
greater than α
This test statistic leads to a decision to...
reject the null
accept the null
fail to reject the null
As such, the final conclusion is that...
There is sufficient evidence to warrant rejection of the claim that the population mean is less than 69.1.
There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 69.1.
The sample data support the claim that the population mean is less than 69.1.
There is not sufficient sample evidence to support the claim that the population mean is less than 69.1.
will anyone answer this question?
To calculate the test statistic, we need to use the formula:
test statistic = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))
In this case, the sample mean (¯x) is 67, the hypothesized mean (μ) is 69.1, the standard deviation (σ) is 8.8, and the sample size (n) is 69. Plugging in the values, we get:
test statistic = (67 - 69.1) / (8.8 / sqrt(69))
≈ -2.840
Therefore, the test statistic for this sample is approximately -2.840.
To calculate the p-value, we need to compare the test statistic to the appropriate distribution. Since the alternative hypothesis (Ha) is one-tailed and the sample mean is smaller than the hypothesized mean, we are looking for the area to the left of the test statistic in the t-distribution. We want the p-value for this area.
Using a statistical table or software, we find that the p-value for a test statistic of -2.840 is approximately 0.0027.
Since the p-value (0.0027) is less than the significance level (0.001), we can conclude that the p-value is less than or equal to α.
Now let's analyze the test statistic:
- Since the test statistic falls in the critical region (to the left of the critical value), we reject the null hypothesis (Ho).
- The test statistic leads to a decision to reject the null hypothesis.
Based on the results, we can conclude:
- There is sufficient evidence to warrant rejection of the claim that the population mean is less than 69.1.