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Stella [2.4K]
3 years ago
12

The average student-loan debt is reported to be $25,235. A student believes that the student-loan debt is higher in her area. Sh

e takes a random sample of 100 college students in her area and determines the mean student-loan debt is $27,524 and the standard deviation is $6,000. Is there sufficient evidence to support the student's claim at a 5% significance level? Preliminary: Is it safe to assume that n ≤ 5 % of all college students in the local area? No Yes Is n ≥ 30 ? Yes No Test the claim: Determine the null and alternative hypotheses. Enter correct symbol and value. H 0 : μ = H a : μ Determine the test statistic. Round to two decimals. t = Find the p -value. Round to 4 decimals. p -value = Make a decision. Fail to reject the null hypothesis. Reject the null hypothesis. Write the conclusion. There is sufficient evidence to support the claim that student-loan debt is higher than $25,235 in her area. There is not sufficient evidence to support the claim that student-loan debt is higher than $25,235 in her area.
Mathematics
1 answer:
yulyashka [42]3 years ago
6 0

Answer:

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 = 25235

For the alternative hypothesis,

µ > 25235

This is a right tailed test.

Since the population standard deviation is not given, the distribution is a student's t.

Since n = 100,

Degrees of freedom, df = n - 1 = 100 - 1 = 99

t = (x - µ)/(s/√n)

Where

x = sample mean = 27524

µ = population mean = 25235

s = samples standard deviation = 6000

t = (27524 - 25235)/(6000/√100) = 3.815

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

p = 0.000119

Since alpha, 0.05 > than the p value, 0.000119, then we would reject the null hypothesis. There is sufficient evidence to support the claim that student-loan debt is higher than $25,235 in her area.

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Step-by-step explanation:

If x is the volume of the first tank, and y is the volume of the second tank, then:

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Solve the system of equations using either substitution or elimination.  Using substitution:

2y + 4 + y = 55

3y + 4 = 55

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A table which shows a possible ratio table for ingredients X and Y for the given number of servings is table 4.

<h3>What is a proportion?</h3>

A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

Mathematically, a direct proportion can be represented the following equation:

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Since the recipe ingredients remain in a constant ratio, we have:

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For table 1, we have:

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