1. A coin-operated drink machine was designed to discharge a mean of 7 ounces of coffee per cup. In a test of the machine, the discharge amounts in 13 randomly chosen cups of coffee from the machine were recorded. The sample mean and the sample standard deviation were 7.08 ounces and 0.22 ounces, respectively. If we assume that the true amounts are normally distributed, is there enough evidence, at the 0.1 level of significance, to conclude that the true mean discharge, µ, differs from 7 ounces? Carry your intermediate computations to at least three decimal places.

No, at the 0.1 level of significance, there is not enough evidence to conclude that the true mean discharge, µ, differs from 7 ounces.

Step-by-step explanation:

We are given that a coin-operated drink machine was designed to discharge a mean of 7 ounces of coffee per cup. In a test of the machine, the discharge amounts in 13 randomly chosen cups of coffee from the machine were recorded.

The sample mean and the sample standard deviation were 7.08 ounces and 0.22 ounces, respectively.

Let = true mean discharge amount

SO, Null Hypothesis, : = 7 ounces  {means that the true mean discharge, µ, does not differs from 7 ounces}

Alternate Hypothesis, : 7 ounces  {means that the true mean discharge, µ, differs from 7 ounces}

The test statistics that will be used here is One-sample t test statistics because we don't know about the population standard deviation;

                T.S.  =    ~

where,   = sample mean discharge amount = 7.08 ounces

              s = sample standard deviation = 0.22 ounces

              n = sample of coffee cups = 13

So, test statistics  =    ~

                               =  1.311

Now at 0.1 significance level, the t table gives critical values between -1.782 and 1.782 at 12 degree of freedom for two-tailed test. Since our test statistics lies within the range of critical values of t so we insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the the true mean discharge, µ, does not differs from 7 ounces.

this story was prepared by jim

mccullaugh in los angeles and

al stewart in new york.

new york the colossal success of "top gun" appears to have dramatically altered madison avenue's

perception of corporate sponsorship

of home video projects.

the paramount home video re- lease, featuring a 60- second diet

pepsi spot, was by no means the

first prerecorded video to carry an advertiser's plug, but it was the

first major theatrical release to do so. in the aftermath of the title's

success, paramount is widely ex- pected to ink a similar deal for

"crocodile dundee" or "star trek

iv" or both.

corporate america's new attraccds push british

recording sales

to 19% gain

london fueled by the compact

disk boom, the value of u.k. manu- facturer shipments of recordings

rose 19% in the 12 -month period ended march 1987, according to the

british phonographic industry.

total value of u.k. shipments for

the period was $755 million for all

configurations. (all value figures

are based on an exchange rate of

$1.68 to the pound sterling.)

cd sales totaled 10.7 million units

worth $121.3 million- compared

with 3.7 million units worth $39.5

million in the prior 12 months -and

accounted for two -thirds of the

overall gain in trade value. at present growth rates, says the bpi, cd

sales for calendar 1987 will reach 20

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step-by-step explanation: