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Chapter 8: Q.19 (page 478)

In complete sentences, explain why the confidence interval in Exercise 8.17 is larger than in Exercise 8.18.

Short Answer

Expert verified

A larger confidence level results in larger areas and larger intervals.

Step by step solution

01

Given Information

Explain why the confidence interval?

02

Explanation

The interval is greater because the level of confidence increased. If the only change made in the analysis is a change in confidence level, then all we are doing is changing how much area is being calculated for the normal distribution. Therefore, a larger confidence level results in larger areas and larger intervals.

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Most popular questions from this chapter

Define the random variable X in words.

Define the random variablesX andx{"x":[[179,180,181,183,186,189,193,196,198,200,202,204,205,207,208,210,211,212,213,214,214,215,215,215,215,215,215,214,212,211,209,207,206,204,203,201,199,198,197,195,194,193,192,191],[226,225,224,221,219,218,217,215,214,213,213,212,212,211,211,211,211,211,211,212,213,214,216,217,220,223,225,227,229,232,233,235,236,238,239,240,241,242,242,243],[164,165,168,176,181,187,192,197,202,205,207,212,215,216,218,219,220,221,222]],"y":[[101,100,100,99,97,96,96,96,96,96,96,97,98,100,100,102,104,105,107,108,109,111,112,113,115,117,119,121,123,124,125,127,127,128,128,129,129,129,129,129,129,129,128,128],[88,89,90,93,95,97,98,100,101,103,104,104,105,107,108,109,110,111,113,114,114,115,116,118,119,120,121,121,121,121,121,121,121,121,120,120,120,120,119,119],[84,84,83,81,80,78,77,77,76,76,75,75,74,73,73,73,72,72,72]],"t":[[0,334,339,357,374,390,408,424,440,457,473,490,506,523,540,557,574,590,606,623,640,657,675,689,706,724,740,756,774,789,806,823,840,857,873,890,907,923,940,957,974,990,1006,1023],[2075,2299,2306,2324,2340,2356,2373,2389,2406,2423,2443,2458,2473,2490,2508,2523,2551,2590,2606,2623,2640,2656,2674,2690,2707,2723,2740,2756,2772,2789,2806,2823,2840,2856,2873,2890,2907,2956,2973,2989],[4121,4332,4340,4356,4373,4389,4406,4423,4440,4456,4473,4489,4506,4523,4539,4557,4573,4598,4656]],"version":"2.0.0"} in words.

The 95% confidence interval is:__________________.

If it were later determined that it was important to be more than 90% confident and a new survey was commissioned, how would it affect the minimum number you need to survey? Why?

Six different national brands of chocolate chip cookies were randomly selected at the supermarket. The grams of fat per serving are as follows: 8;8;10;7;9;9. Assume the underlying distribution is approximately normal.

a. Construct a 90%confidence interval for the population mean grams of fat per serving of chocolate chip cookies

sold in supermarkets.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

b. If you wanted a smaller error bound while keeping the same level of confidence, what should have been changed in the study before it was done?

c. Go to the store and record the grams of fat per serving of six brands of chocolate chip cookies.

d. Calculate the mean.

e. Is the mean within the interval you calculated in part a? Did you expect it to be? Why or why not?
See all solutions

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