A 16\dfrac1216 2 1 16, start fraction, 1, divided by, 2, end fraction kilometer stretch of road needs repairs. Workers can rep
1 answer:
Answer:
It will take weeks to complete the repair of the stretch of road.
Step-by-step explanation:
Given:
Length of the roads that need repairs =
Length of the road workers can repair in a week =
To find the number of weeks will it take to repair this stretch of road.
Solution:
Unit rate of workers to repair roads = per week.
Total length of the roads to repair =
The number of weeks it will take to repair of road by workers can be given as:
⇒
<em>In order to divide mixed numbers, we convert them first to fractions.</em>
⇒
<em>To divide fractions, we take reciprocal of the divisor and replace division with multiplication:</em>
⇒
⇒
We reconvert the fraction to mixed number.
⇒ weeks
Thus, it will take weeks to complete the repair of the stretch of road.
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Answer:
No, there is not enough evidence to support the claim that true average task time with armor is less than 2 seconds.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that true average task time with armor is less than 2 seconds.
Then, the null and alternative hypothesis are:
The significance level is 0.01.
The sample has a size n=52.
The sample mean is M=1.95.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.2.
The estimated standard error of the mean is computed using the formula:
Then, we can calculate the t-statistic as:
The degrees of freedom for this sample size are:
This test is a left-tailed test, with 51 degrees of freedom and t=-1.803, so the P-value for this test is calculated as (using a t-table):
As the P-value (0.039) is bigger than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that true average task time with armor is less than 2 seconds.
Answer:
The sample consisting of 64 data values would give a greater precision.
Step-by-step explanation:
The width of a (1 - <em>α</em>)% confidence interval for population mean μ is:
So, from the formula of the width of the interval it is clear that the width is inversely proportion to the sample size (<em>n</em>).
That is, as the sample size increases the interval width would decrease and as the sample size decreases the interval width would increase.
Here it is provided that two different samples will be taken from the same population of test scores and a 95% confidence interval will be constructed for each sample to estimate the population mean.
The two sample sizes are:
<em>n</em>₁ = 25
<em>n</em>₂ = 64
The 95% confidence interval constructed using the sample of 64 values will have a smaller width than the the one constructed using the sample of 25 values.
Width for n = 25:
Width for n = 64:
Thus, the sample consisting of 64 data values would give a greater precision