Solution :
Assuming
We have to test
Against
Level of significance,
= 420.6107
Under , the t-statistics is as follows:
= 0.90
DF = (25 + 20 - 2)
= 43
P-value of the test = 0.375
Since the p value is more than 0.05, we fail to reject our null hypothesis.
There is no difference between then mean tensile strength of the ropes that is produced in the Bozeman and Challis.
Answer:
The 95% confidence interval for true proportion of red candies is (5%, 27%).
The true proportion of red candies made by the company is different from 33%.
Step-by-step explanation:
The hypothesis to determine whether the claim made by the candy company is correct or not is:
<em>H</em>₀: The true proportion of red candies made by the company is 33%, i.e. <em>p</em> = 0.33.
<em>Hₐ</em>: The true proportion of red candies made by the company is different from 33%, i.e. <em>p</em> ≠ 0.33.
A (1 - <em>α</em>)% confidence interval can be constructed to check this claim.
The decision rule is:
If the confidence interval consists the null value then the null hypothesis will not be rejected. Otherwise it will be rejected.
The (1 - <em>α</em>)% confidence interval for population proportion is:
The information provided is:
<em>n</em> = 42
<em>X</em> = number of red candies = 7
Compute the sample proportion of candies that are red as follows:
The critical value of <em>z</em> for 95% confidence level is:
*Use a <em>z</em>-table for the critical value.
Compute the 95% confidence interval for true proportion of red candies as follows:
The 95% confidence interval for true proportion of red candies is (5%, 27%).
The confidence interval does not contains the null value.
Thus, the null hypothesis will be rejected at 5% level of significance.
Conclusion:
The true proportion of red candies made by the company is different from 33%.