The figures below represent the prices (in dollars) for both paper shredders and calculators. At the 0.10 level of significance, can it be concluded that the variance in price differs between the two types of machines?
Paper shredders | Calculators
-----------------------------------
75 115 118 287 | 110 140 165 90 230
250 300 50 | 97 269
|
Thank You very much in advance for any help.
My apologies, the figure got messed up
Paper shredders
---------------
75 115 118 287
250 300 50
Calculators
--------------
110 140 165 90 230
97 269
This is a hypothesis test involving variances.
Sample size for paper shredders = 7
Variance = ? (you will need to calculate the variance from the data given)
degrees of freedom = 6 (df = n - 1)
Sample size for calculators = 7
Variance = ? (you will need to calculate the variance from the data given)
degrees of freedom = 6
Determine the critical or cutoff value to reject the null using an F-distribution table at 0.10 level of significance using the above information.
Test statistic = variance of paper shredders divided by variance of calculators
Once you have the test statistic, compare to the critical value you found from the table. If the test statistic exceeds the critical value, reject the null (difference). If the test statistic does not exceed the critical value, do not reject the null (no difference).
I hope this will help.
To determine whether the variance in price differs between paper shredders and calculators, we can use a two-sample F-test. The F-test is a statistical test that compares the variances of two samples.
Here's how you can perform the F-test:
Step 1: State the hypotheses:
- Null hypothesis (H0): The variance in price is the same for paper shredders and calculators.
- Alternative hypothesis (Ha): The variance in price differs between paper shredders and calculators.
Step 2: Calculate the sample variances:
- Calculate the variance for the paper shredders sample: var1.
- Calculate the variance for the calculators sample: var2.
Step 3: Set the significance level:
- The significance level is given as 0.10 (or 10%).
Step 4: Calculate the F-statistic:
- The F-statistic is calculated as the ratio of the larger sample variance to the smaller sample variance: F = var1 / var2.
Step 5: Determine the critical F-value:
- Use the degrees of freedom (df1, df2) to find the critical F-value from the F-table or calculate it using a statistical software.
Step 6: Compare the calculated F-statistic with the critical F-value:
- If the calculated F-statistic is greater than the critical F-value, reject the null hypothesis.
- If the calculated F-statistic is less than or equal to the critical F-value, fail to reject the null hypothesis.
Note: The degrees of freedom (df) for each sample are calculated as the number of observations minus one.
By following these steps, you should be able to determine whether the variance in price differs significantly between paper shredders and calculators at the 0.10 level of significance.