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1 answer:
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Answer:
Our decision rule will be to reject The null hypothesis H0 if the test statistic is less than -1.645, or if it is greater than +1.645.
Step-by-step explanation:
The hypotheses would be;
Null hypothesis;H0: μ = 500
Alternative hypothesis;Ha: μ ≠ 500
Since it's two - tailed at 0.1 level of significance, then each tail will contain 5% or 0.05. From the z-table attached, the corresponding critical value of 0.05 is approximately 1.645 standard deviations from the mean.
Thus, our decision rule will be to reject The null hypothesis H0 if the test statistic is less than -1.645, or if it is greater than +1.645.
Answer:
- (-1, -32) absolute minimum
- (0, 0) relative maximum
- (2, -32) absolute minimum
- (+∞, +∞) absolute maximum (or "no absolute maximum")
Step-by-step explanation:
There will be extremes at the ends of the domain interval, and at turning points where the first derivative is zero.
The derivative is ...
h'(t) = 24t^2 -48t = 24t(t -2)
This has zeros at t=0 and t=2, so that is where extremes will be located.
We can determine relative and absolute extrema by evaluating the function at the interval ends and at the turning points.
h(-1) = 8(-1)²(-1-3) = -32
h(0) = 8(0)(0-3) = 0
h(2) = 8(2²)(2 -3) = -32
h(∞) = 8(∞)³ = ∞
The absolute minimum is -32, found at t=-1 and at t=2. The absolute maximum is ∞, found at t→∞. The relative maximum is 0, found at t=0.
The extrema are ...
- (-1, -32) absolute minimum
- (0, 0) relative maximum
- (2, -32) absolute minimum
- (+∞, +∞) absolute maximum
_____
Normally, we would not list (∞, ∞) as being an absolute maximum, because it is not a specific value at a specific point. Rather, we might say there is no absolute maximum.
Complete Question
A survey is planned to estimate the proportion of voters who support a proposed gun control law. The estimate should be within a margin of error of ±5% with 90% confidence, and we do not have any prior knowledge about the proportion who might support the law. How many people need to be included in the sample?
Round your answer up to the nearest integer.
sample size = _____
Answer:
The sample size is
Step-by-step explanation:
From the question we are told that
The margin of error is E = 5% = 0.05
Generally given that there was no prior knowledge about the proportion of who might support the law, we will assume the sample proportion to be
From the question we are told the confidence level is 90% , hence the level of significance is
=>
Generally from the normal distribution table the critical value of is
Generally the sample size is mathematically represented as
=>
=>