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pashok25 [27]
3 years ago
15

Svetlana's hair is 4 cm long her hair grows 1.5 sm per month svetlana wants her hair to grow so that it is at least 7 cm long Wr

ite an inequality to determine the number of months m it will take svetlana hair to grow so it is at least 7 centimeters long
Mathematics
1 answer:
Radda [10]3 years ago
5 0
Y=4+1.5x

7=4+1.5x

3=1.5x

2=x
It will take at least two months for her hair to be 7 cm
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Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 106

For the alternative hypothesis,

µ > 106

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Since no population standard deviation is given, the distribution is a student's t.

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Degrees of freedom, df = n - 1 = 241 - 1 = 240

t = (x - µ)/(s/√n)

Where

x = sample mean = 109

µ = population mean = 106

s = samples standard deviation = 8.3

a) test statistic, t = (109 - 106)/(8.3/√241) = 5.61

We would determine the p value using the t test calculator. It becomes

p = 0.00001

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b) Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × s/√n

Where

s = sample standard deviation

n = number of samples

From the information given, the population standard deviation is unknown, hence, we would use the t distribution to find the z score

df = 240

Since confidence level = 95% = 0.95, α = 1 - CL = 1 – 0.95 = 0.05

α/2 = 0.05/2 = 0.025

the area to the right of z0.025 is 0.025 and the area to the left of z0.025 is 1 - 0.025 = 0.975

Looking at the t distribution table,

z = 1.6512

Margin of error = 1.6512 × 8.3/√241

= 0.88

Confidence interval = 109 ± 0.88

7 0
3 years ago
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