statistics

posted by .

it is stated that the standard deviation sample of the is 7.6 (n = 26). Test the claim to a significance level of 0.10 that the population standard deviation was greater than 7.0. Round all answers to 3 decimal places.

• statistics -

Null and alternative hypotheses:
Ho: The population standard deviation is = 7.0
Ha: The population standard deviation is > 7.0

Data given:
sample standard deviation = 7.6
level of significance = 0.10
n = 26

The test statistic used in making a decision is the chi-square.
Here's the formula:

chi-square = (sample size - 1)(sample variance)/(value specified in the null hypothesis)

Note: Convert both standard deviations to variances (7.0 and 7.6) when working with the formula. Remember that standard deviation is the square root of the variance; therefore, variance is standard deviation squared.

Degrees of freedom is equal to n - 1, which is 25.

Checking a chi-square table using significance level = 0.10 with 25 degrees of freedom, find the critical value. If the test statistic exceeds the critical value from the chi-square table, then the null is rejected. If the test statistic does not exceed the critical value from the table, then the null cannot be rejected and there is not enough evidence to support the claim that the population standard deviation is greater than 7.0 grams.

I hope this will help get you started.

• Correction -

If the test statistic does not exceed the critical value from the table, then the null cannot be rejected and there is not enough evidence to support the claim that the population standard deviation is greater than 7.0. (The word "grams" should not have been included.)

Sorry for any confusion.

Similar Questions

1. Statistics

Use a x squared-test to test the claim about the population variance or standard deviation at the given level of significance and using the given sample statistics. Claim: ơ2 ≤ 60; α = 0.025. Sample statistics: s2 = …
2. Statistics

Use a chi-squared test to test the claim about the population variance or standard deviation at the given level of significance and using the given sample statistics. Claim: ơ2 ≤ 60; α = 0.025. Sample statistics: s2 …
3. statistics

A sample of 40 observations is selected from one approximately normal population. The sample mean is 102 and the sample standard deviation is 5. A sample of 50 observations is selected from a second source. The sample mean is 99 and …
4. statistics

A sample of 40 observations is selected from one approximately normal population. The sample mean is 102 and the sample standard deviation is 5. A sample of 50 observations is selected from a second source. The sample mean is 99 and …
5. statistics

Prep Courses? Scores for men (nationwide) on the verbal portion of the SAT test are normally distributed with a mean of 509 and a standard deviation of 112. Randomly selected men are given the Columbia review course before taking the
6. statistics

Given a sample size of 38, with sample mean 660.3 and sample standard deviation 95.9 we are to perform the following hypothesis test. Null Hypothesis H0: ƒÊ = 700 Alternative Hypothesis H0: ƒÊ ‚ 700 At significance level 0.05 …
7. Statistics

This is the first question..... For a population that has a standard deviation of 10, figure the standard deviation of the distribution of means for samples of size- (b) 3. This is the second question....For each of the following samples …
8. statistics

it is stated that the standard deviation sample of the is 7.6 (n = 26). Test the claim to a significance level of 0.10 that the population standard deviation was greater than 7.0. Round all answers to 3 decimal places.
9. Statistics

A random sample of 150 pumpkins is obtained and the mean circumference is found to be 45 cm. Assuming that the population standard deviation is known to be 1.8 cm, use a 0.03 significance level to test the claim that the mean circumference …
10. Statistics

I don't understand this at all.. Assume that the weights of Chinook Salmon in the Columbia River are normally distributed. You randomly catch and weigh 40 such salmon. The mean weight from your sample is 24.1 pounds with a standard …

More Similar Questions