How many commuters must be randomly selected to estimate the mean driving time of Chicago commuters? We want 95% confidence that
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Answer:
(a) Null Hypothesis, :
41
Alternate Hypothesis, :
> 41
(b) The value of z test statistics is 1.08.
(c) We conclude that the mean sunspot activity during the Spanish colonial period was lesser than or equal to 41.
Step-by-step explanation:
We are given that in a random sample of 40 such periods from Spanish colonial times, the sample mean is x¯ = 47.0. Previous studies of sunspot activity during this period indicate that σ = 35.
It is thought that for thousands of years, the mean number of sunspots per 4-week period was about µ = 41.
Let = <u><em>mean sunspot activity during the Spanish colonial period.</em></u>
(a) Null Hypothesis, :
41 {means that the mean sunspot activity during the Spanish colonial period was lesser than or equal to 41}
Alternate Hypothesis, :
> 41 {means that the mean sunspot activity during the Spanish colonial period was higher than 41}
The test statistics that would be used here <u>One-sample z test statistics</u> as we know about the population standard deviation;
T.S. = ~ N(0,1)
where, = sample mean = 47
σ = population standard deviation = 35
n = sample of periods from Spanish colonial times = 40
So, <em><u>the test statistics</u></em> =
= 1.08
(b) The value of z test statistics is 1.08.
(c) <u>Now, the P-value of the test statistics is given by;</u>
P-value = P(Z > 1.08) = 1 - P(Z < 1.08)
= 1 - 0.8599 = <u>0.1401</u>
Since, the P-value of the test statistics is higher than the level of significance as 0.1401 > 0.05, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis</u>.
Therefore, we conclude that the mean sunspot activity during the Spanish colonial period was lesser than or equal to 41.
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<h2>Hope this helps!</h2>
Answer:
The legs are 1.9 feet long
And the base is 1.1 feet long.
Step-by-step explanation:
Firstly, you need to find the value of x.
You need to add all the sides together:
2x - 0.3 + 2x - 0.3 + x
Simplified =
5x - 0.6
And this equals 4.9:
5x - 0.6 = 4.9
Next, you need to move the -0.6 over to the other side, making sure to make it a positive:
5x = 4.9 + 0.6
5x = 5.5
Now divide each side by 5:
x = 1.1
As the image is unclear of what side you are finding the length of:
2x - 0.3 = 1.9 feet long
And the base is 1.1 feet long.
<h2>Hope this helps!</h2>