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Alexxandr [17]
3 years ago
7

I really need assistance with this question

Mathematics
1 answer:
Nastasia [14]3 years ago
6 0

Answer:

first

Step-by-step explanation:

Lumen

Managerial Accounting

Chapter 5: Cost Behavior and Cost-Volume-Profit Analysis

5.6 Break – Even Point for a single product

Finding the break-even point

A company breaks even for a given period when sales revenue and costs charged to that period are equal. Thus, the break-even point is that level of operations at which a company realizes no net income or loss.

A company may express a break-even point in dollars of sales revenue or number of units produced or sold. No matter how a company expresses its break-even point, it is still the point of zero income or loss. To illustrate the calculation of a break-even point watch the following video and then we will work with the previous company, Video Productions.

Before we can begin, we need two things from the previous page: Contribution Margin per unit and Contribution Margin RATIO. These formulas are:

Contribution Margin per unit = Sales Price – Variable Cost per Unit

Contribution Margin Ratio = Contribution margin (Sales – Variable Cost)

Sales

Break-even in units

Recall that Video Productions produces DVDs selling for $20 per unit. Fixed costs

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Answer:

(a) Customer will not purchase the light bulbs at significance level of 0.05

(b) Customer will purchase the light bulbs at significance level of 0.01 .

Step-by-step explanation:

We are given that Light bulbs of a certain type are advertised as having an average lifetime of 750 hours. A random sample of 50 bulbs was selected,  and the following information obtained:

Average lifetime = 738.44 hours and a standard deviation of lifetimes = 38.2 hours.

Let Null hypothesis, H_0 : \mu = 750 {means that the true average lifetime is same as what is advertised}

Alternate Hypothesis, H_1 : \mu < 750 {means that the true average lifetime is smaller than what is advertised}

Now, the test statistics is given by;

       T.S. = \frac{Xbar-\mu}{\frac{s}{\sqrt{n} } } ~ t_n_-_1

where, X bar = sample mean = 738.44 hours

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So, test statistics = \frac{738.44-750}{\frac{38.2}{\sqrt{50} } } ~ t_4_9

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(a) Now, at 5% significance level, t table gives critical value of -1.6768 at 49 degree of freedom. Since our test statistics is less than the critical value of t, so which means our test statistics will lie in the rejection region and we have sufficient evidence to reject null hypothesis.

Therefore, we conclude that the true average lifetime is smaller than what is advertised and so consumer will not purchase the light bulbs.

(b) Now, at 1% significance level, t table gives critical value of -2.405 at 49 degree of freedom. Since our test statistics is higher than the critical value of t, so which means our test statistics will not lie in the rejection region and we have insufficient evidence to reject null hypothesis.

Therefore, we conclude that the true average lifetime is same as what it has been advertised and so consumer will purchase the light bulbs.

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