Please help with this and explain how to do it, I'll give 15 points
1 answer:
Answer:
Option (4).
Step-by-step explanation:
Outer diameter of the hollow metallic ball = 10 centimeters
Outer radius of this ball = = 5 cm
Volume of the outer ball =
=
Inner radius of the hollow metallic ball = (5 - 1) = 4 cm
Volume of the inner hollow ball =
Volume of the metal used in the metallic ball =
=
=
Therefore, expression given in option (4) will be used to measure the volume of the hollow metallic ball.
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Answer:
a) The pooled proportion is p=0.3.
b) P-value = 0.000078
c) Lower bound = 0.0556
d) Upper bound = 0.1644
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that the accident proportions differ between the two age groups .
Then, the null and alternative hypothesis are:
The significance level is 0.05.
The sample 1, of size n1=500 has a proportion of p1=0.36.
The sample 2, of size n2=600 has a proportion of p2=0.25.
.
The difference between proportions is (p1-p2)=0.11.
The pooled proportion, needed to calculate the standard error, is:
The standard error for the difference between proportions can now be calculated as:
The estimated standard error of the difference between means is computed using the formula:
Then, we can calculate the z-statistic as:
This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):
As the P-value (0.000078) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the accident proportions differ between the two age groups.
If we want to calculate the bounds of a 95% confidence interval, we start by calculating the margin of error.
For a 95% CI, the critical value for z is z=1.96.
Then, the margin of error is:
Then, the lower and upper bounds of the confidence interval are:
The 95% confidence interval for the population mean is (0.0556, 0.1644).