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Chapter 8: Q. 57 (page 480)

The data in the Table are the result of a random survey of 39national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X=the number of colors on a national flag.

XFreq.11273184756

Construct a 95%confidence interval for the true mean number of colors on national flags.

The 95%confidence interval is_____.

Short Answer

Expert verified

The 95%confidence interval s islocalid="1649351039594" 2.92,3.59.

Step by step solution

01

Given Information

The data in the Table are the result of a random survey of 39national flags (with replacement between picks) from various countries.

XFreq.11273184756

02

Explanation

Now we need to find the sample mean

Mean=X炉=鈭�fixini

Mean=12739=3.26

The standard deviation will be,

Standard Deviation=鈭�fixi2鈭�鈭�fuxi2nn鈭�1

=453鈭�12723938

=1.02

Confidence Interval will be,

Confidence Interval=X炉卤Zn鈭�1,a2脳Sn

=3.26卤t38,0.052脳1.0239

3.26卤2.024脳1.0239

localid="1649350961439" =[2.92,3.59]

Thus,

Lower Bound =2.92

Upper Bound=3.59

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Most popular questions from this chapter

In one complete sentence, explain what the interval means.

Using the same mean, standard deviation, and sample size, how would the error bound change if the confidence level were reduced to 90%? Why?

Which distribution should you use for this problem?

Define the random variable X炉{"x":[[4,22,36],[6,35],[5.647456684472792,6.517307794504744,6.517307794504744,8.257010014568648,9.1268611246006,9.996712234632552,12.606265564728409,13.476116674760362,14.345967784792315,16.08567000485622,16.95552111488817,17.825372224920123,18.695223334952075,20.43492555501598,21.30477666504793,22.174627775079884,23.044478885111836,23.914329995143788,24.78418110517574,25.654032215207693,26.523883325239645,27.393734435271597,27.393734435271597,28.26358554530355,29.1334366553355,29.1334366553355,30.003287765367453,30.873138875399405,31.742989985431358,32.61284109546331]],"y":[[9,59,116],[115,9],[-7.088088802556169,-7.088088802556169,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-7.957939912588121,-8.827791022620074,-8.827791022620074,-8.827791022620074,-9.697642132652026,-9.697642132652026,-9.697642132652026,-9.697642132652026,-9.697642132652026]],"t":[[0,0,0],[0,0],[1648475418436,1648475418678,1648475418692,1648475418709,1648475418727,1648475418743,1648475418760,1648475418776,1648475418791,1648475418810,1648475418826,1648475418842,1648475418859,1648475418875,1648475418892,1648475418910,1648475418925,1648475418942,1648475418965,1648475419009,1648475419026,1648475419076,1648475419105,1648475419118,1648475419134,1648475419146,1648475419161,1648475419180,1648475419242,1648475419292]],"version":"2.0.0"}in words.

The data in the Table are the result of a random survey of 39national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X=the number of colors on a national flag.

XFreq.11273184756

Construct a 95%confidence interval for the true mean number of colors on national flags.

Calculate the following:

a. lower limit

b. upper limit

c. error bound
See all solutions

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