A company would like to advertise that their new fishing lin

A company would like to advertise that their new fishing line has an average breaking strngth greater that 16 kilograms. The lines breaking strength is known to vary in the population on average 3.3 kilograms. To test the breaking strength of their new product the company takes a random sample of 50 lines, the average strength measure is 17.1 kilograms. Use a significance level of 0.05.

a) What is the parameter of interest?

b) State the null and alternative hypothesis

c) State the conditions for inference. Include reasoning as to why they are or are not met.

d) Calculate the test statistic SHOW WORK

e) Give the apporpriate p-value and state whether it is one-sided or two-sided

f) Calculate the appropriate 95% confidence interval and show work

g) Finally using the results, summarize your conclusions in the context of the problem.

Solution

a) What is the parameter of interest?

mu = the population average breaking strngth

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b) State the null and alternative hypothesis

Null hypothesis: mu =16

Alternative hypothesis: mu >16

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c) State the conditions for inference. Include reasoning as to why they are or are not met.

We need to assume that the population mean follows normal distriubtion.

Since the sample size is larger than 30, we can use normal distribution approximated.

So they are met

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d) Calculate the test statistic

Z=(xbar-mu)/(s/vn)

=(17.1-16)/(3.3/sqrt(50))

=2.36

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e) Give the apporpriate p-value and state whether it is one-sided or two-sided

It is a one-tailed test.

So the p-value= P(Z>2.36) =0.0091 (from standard normal table)

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f) Calculate the appropriate 95% confidence interval and show work

Given a=0.05, Z(0.025) = 1.96 (from standard normal table)

So 95% confidecen interval is

xbar +/- Z*s/vn

--> 17.1 +/- 1.96*(3.3/sqrt(50))

--> (16.18529, 18.01471)

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g) Finally using the results, summarize your conclusions in the context of the problem.

Since the p-value is less than 0.05, we reject Ho.

So we can conclude that their new fishing line has an average breaking strngth greater that 16 kilograms.