A fenced in rectangular region with the dimensions 4 yards by 8 yards is suddenly expanded by the same distance in each dimensio
1 answer:
Answer:
The distance added to each dimension is 2 yards.
Step-by-step explanation:
The initial dimensions of the rectangular fence is 8 yards by 4 yards.
The initial area of the rectangular fence = area of a rectangle
area of a rectangle = length x width
So that,
The initial area of the fence = 8 x 4
= 32
The initial area of the fence is 32 square yards.
But, with the new dimensions, area = 60 square yards.
(4 + x) x (8 + x) = 60
+ 12x + 28 = 60
+ 12x - 32 = 0
(x + 14) = 0 or (x - 2) = 0
x = -14 or x =2
Thus, x = 2
The distance added to each dimension is 2 yards.
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Answer:
Yes, this provide enough evidence to show a difference in the proportion of households that own a desktop.
Step-by-step explanation:
We are given that National data indicates that 35% of households own a desktop computer.
In a random sample of 570 households, 40% owned a desktop computer.
<em><u>Let p = population proportion of households who own a desktop computer</u></em>
SO, Null Hypothesis, : p = 25% {means that 35% of households own a desktop computer}
Alternate Hypothesis, : p
25% {means that % of households who own a desktop computer is different from 35%}
The test statistics that will be used here is <u>One-sample z proportion</u> <u>statistics</u>;
T.S. = ~ N(0,1)
where, = sample proportion of 570 households who owned a desktop computer = 40%
n = sample of households = 570
So, <u><em>test statistics</em></u> =
= 2.437
<em>Since, in the question we are not given with the level of significance at which to test out hypothesis so we assume it to be 5%. Now at 5% significance level, the z table gives critical values of -1.96 and 1.96 for two-tailed test. Since our test statistics doesn't lies within the range of critical values of z so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.</em>
Therefore, we conclude that % of households who own a desktop computer is different from 35%.