Chapter 8

 

  1. In the drought year 1988, statements were made that over half of

     Indiana corn producers did not get back from their corn crop the

     money they put into seed, fertilizer, etc. To check this, a random

     sample of 800 farms is chosen and a brief audit is made on each of

     these farms. Of these farms, 405 did not recover their costs from

     their corn crops.

      a. Is this good evidence for the claim in the first sentence? (State

         hypotheses, carry out a test, give the P-value, and state your

         conclusion.)

      b. Give a 95% confidence interval for the proportion of producers

         who did not get back their money.

 

  2. A new variety of apple is intended to resist cedar apple rust. A

     horticulturist grows 100 trees of the new strain and 200 of the

     parent strain under the same field conditions. At the end of three

     years, each tree is checked by a researcher and classified as

     "seriously infected" or "not seriously infected" by rust. The

     results show that 45 trees of the new strain and 123 of the parent

     strain are seriously infected.

     a. Give a 99% confidence interval for the population proportion

        infected (parent strain) minus population proportion infected

        (new strain).

    

  3. A new variety of apple is intended to resist cedar apple rust. A

     horticulturist grows 50 trees of the new strain and 100 of the

     parent strain under the same field conditions. At the end of three

     years, each tree is checked by a researcher and classified as

     "seriously infected" or "not seriously infected" by rust. The

     results show that 22 trees of the new strain and 61 of the parent

     strain are seriously infected. Is there significant evidence that a

     smaller proportion of the new strain becomes infected? (State null

     and alternative hypotheses, report the test statistic and the

     P-value and state your conclusion.)

 

  4. A nursery advertises that 95% of its stock survives transplanting.

     An apartment complex purchases 120 trees from this nursery, and 11

     do not survive.

     a. Is this evidence that in fact a smaller proportion percentage

        than 95% of trees sold by the nursery survive? (State

        hypotheses, carry out the test, give the P-value, and state your

        conclusion.)

     b. Give a 90% confidence interval for the proportion of trees that

        survive.

  5. Is there significant evidence that the proportion of people with

     cholesterol level less than or equal to 240 differ in the two

     different populations from which the random samples I and II below

     are drawn? (State hypotheses, carry out the test, give the P-value,

     and state your conclusion.)

    

                     I                     II

          283  248  280  230  258  204  270  307  368

          165  234  264  274  229  189  245  220  299

          171  243  310  289  230  220  389  253  189

          202  294  226  219  293  229  269  208  218

          245  312  321  253  208  194  218  280  183

          261  206  285  306  191  258  245  196  255

          299  325  269  219  258  295  243  198  270

          208  260  165  236  196  216  271  227  208

          220  276  276  249  204  198  246  270  306

          208  271  199  206  323  148  194  194  198

 

  6. In an effort to determine what percent of Americans live on farms, a

     polling organization selects a random sample of 500 Americans. Of

     this sample, 26 live on farms.

     a. Give a 95% confidence interval for the proportion of Americans

        who now live on farms.

     b. Would the margin of error of your confidence interval increase or

        decrease if you increased the sample size to 1500 persons?

 

  7.  Below are the weights of a sample of eggs from each of two egg

     producers (I and II).  We want to know whether the proportions of

     eggs supplied by these producers that weigh between 59 and 61 grams

     (including both) are different.

    

            I         II

          58  57  60  58  63

          60  60  61  64  63

          60  61  61  62  59

          59  59  60  62  62

          61  62  62  60  61

          59  61  63  59  60

          62  59  59  64  60

          61  60  58  59  64

          62  58  60  62  62

          61  61  63  60  58

    

     Is there significant evidence at 1% level that the proportions are

     different?  (Be sure to state hypotheses.)

 

  8. In an opinion poll, 25% of 200 people sampled said that they were

     strongly opposed to having a state lottery.  The standard error of

     the sample proportion is approximately

     (a) .03

     (b) .25

     (c) .00094

     (d) 6.12

     (e) .06

  9. You want to design a study to estimate the proportion of students on

     your campus who agree with the statement, "The student government is

     an effective organization for expressing the needs of students to

     the administration."  You will use a 95% confidence interval and you

     would like the margin of error to be .05 or less.  The minimum

     sample size required is approximately

     (a) 22

     (b) 1795

     (c) 385

     (d) 271

     (e) none of the above

 

 10. According to the 1987 Census of Agriculture, 8% of American farms

     are at least 1000 acres in size.  The size of farms varies from

     state to state depending on the type of agriculture that

     predominates.  You are conducting a sample survey of farms in

     Indiana based on a simple random sample of 400 farms in the state.

     You find that 15 of the farms in the sample are at least 1000 acres

     in size.  Estimate the proportion of all Indiana farms that exceed

     1000 acres, with 90% confidence.