�One Sample Inference on Means� Test

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�One Sample Inference on Means� Test Powered By Docstoc
					Hypothesis Tests with Means                                            Please DO NOT WRITE on this test!
AP Statistics                                                          4 points each

1) If you are testing the hypotheses statements H0:  = 56 & Ha:  < 56, then you should perform a
   a) right-tail test          b) left-tail test             c) two-tail test              d) none of the above.

2) A botanist is interested in testing the H0:  = 3.5 cm versus Ha:  > 3.5 cm, where  is the true mean petal
length of one variety of flowers. A random sample of 50 petals gives significant results (rejects H 0) at a 5
percent level of significance. Which of the following statements about the confidence interval to estimate the
mean petal length is true?
  a) A 90% confidence interval contains the specified mean length of 3.5
  b) A 90% confidence interval does not contain the specified mean length of 3.5.
  c) The specified mean length of 3.5 is in the center of a 90% confidence interval.
  d) Not enough information is available to answer the question.

3) A farmer wants to know whether a new fertilizer has increased the mean weight of his apples. With the old
fertilizer, the mean weight was 4.0 ounces per apple. The weights of apples are approximately normally
distributed. The farmer takes a random sample of 16 apples and computes a mean of 4.3 ounces with a standard
deviation of 0.6 ounces. Which of the following gives a correct p-value?
  a) .0228             b) .0455               c) .0639                d) .0320         e) cannot be determined

4) In performing a two-sided hypothesis test, you calculate that the test statistic t = -2.4. If the sample size
is 16, what is the appropriate p-value?
   a) .0149             b) .0298              c) .9851               d) .0082                 e) .0164

5) Which of the following statements about hypotheses is true?
  a) The two possible conclusions in a hypothesis test are “accept H 0” and “accept Ha”.
  b) If the null hypothesis is not rejected, then there is strong statistical evidence that the null hypothesis is
      true.
  c) The fundamental idea behind hypothesis testing is to reject H 0 only when the observed sample is very
      unlikely to have occurred when H0 is true.
  d) The null hypothesis should be rejected when the p-value is larger than the significance level of the test.
  e) The selection of Ha depends on the numerical values of the data or sample mean.

Use for questions 6 & 7: A random sample of AA batteries was tested to see how long they would last in toys.
The following computer output displays the results from the hypothesis test of H0:  = 4.5 versus Ha:   4.5.
The assumptions for inference were met.  = .05

         Variable Sample Mean   Std. Err.   DF   T-Stat     P-value

         Hours          3.575 0.4633663     15 -1.9962608   0.0644


6) What was the sample size?
  a) 15              b) 4.5                      c) .0644              d) 16                   e) 3.575

7) Which of the following is a valid conclusion?
  a) The mean battery life is less than 4.5 hours since the sample mean is less than the hypothesized mean.
  b) The mean battery life is not equal to 4.5 hours since the sample mean is less than the hypothesized mean.
  c) Since the p-value > , the mean battery life is not equal to 4.5 hours.
  d) Since the p-value > , there is insufficient evidence to say the mean battery life is not equal to 4.5 hours.
  e) Since the p-value > , there is insufficient evidence to say the mean battery life is less than to 4.5 hours.
8) A researcher believes a population of fish has a normal distribution with a mean weight of 3.4 kg. She takes
a random sample of 30 fish and finds that the mean is 3 kg with a standard deviation of 0.8 kg. What is the p-
value for the test statistic testing H0 :   3.4 against Ha :   3.4 ?
  a)   .0062           b) .0104                c) .0052               d) .0031                e) .0041

9) A significant test allows you to reject H0 at the 0.05 level of significance. Which of the following
statements is true?
  a) You can reject H0 at the 0.01 level of significance.
  b) You can accept Ha at the 0.05 level of significance.
  c) You can fail to reject Ha at the 0.05 level of significance.
  d) You can reject H0 at the 0.10 level of significance.
  e) You can fail to reject H0 at the 0.01 level of significance.

10) Which of the following statements about matched-pairs analysis is false?
  a) In a matched-pairs analysis, you use a t-test procedure.
  b) In a matched-pairs analysis, the two original samples are said to be dependent on each other.
  c) In a matched-pairs analysis, the distribution of differences should be approximately normally distributed.
  d) In a matched-pairs analysis, you first find the difference of the paired data from the two original
     samples before performing the analysis.
  e) In a matched-pairs analysis, the boxplots of each of the two original samples must be approximately
     symmetrical.

11) A boat manufacturer claims that a particular boat and motor combination will burn no more than 4 gallons of
fuel per hour. A consumer group believes that the manufacturer under-rated the gasoline usage. A random
sample of 36 of these boats results in a mean of 4.09 gallons per hour with standard deviation of 0.24 gallons
per hour. Which of the following is appropriate for calculating the test statistic?
          4.09  4                            4  4.09                               4.09  4
  a) t            ;df  36            b) t           ;df  35               c) t           ;df  35
           .24                                .24                                    .24
               36                                  36                                     36
          4  4.09                            4  4.09
  d) t            ;df  35            e) z 
          .24                                  .24
               35                                   36

12) A drug company claims that the mean time it takes their antihistamine to take effect is 15 minutes. A
random sample of 21 volunteers found that the mean time it takes the antihistamine to appear in the blood is
15.8 minutes with standard deviation 1.3 minutes. Which of the following would test the alternative hypothesis
that the company’s claim is not 15 minutes?
  a) a one-sided t-test with df = 21                 d) a two sided z-test
  b) a one-sided t- test with df = 20                e) a two-sided t-test with df = 20
  c) a one-sided z-test

13) Which of the calculated values of a test statistic would have the smallest p-value?
  a) z = 3.05          b) t = 3.05; df = 10            c) t = 3.05; df = 15           d) t = 3.05; df = 30

14) A department store at a large mall claims that, on average, over 500 people shop at the store per day.
Which of the following hypotheses should be used to test this claim?
  a) H0 :   500 and Ha :   500                     d) H0 :   500 and Ha :   500
  b)   H0 :   500 and Ha :   500                   e) H0 : x  500 and Ha : x  500
  c)   H0 : x  500 and Ha : x  500
15) Which of the following is a correct interpretation of a test statistic?
  a) It is the probability of getting a statistic that extreme or more extreme.
  b) It is the number of deviations that the statistic is above or below the parameter.
  c) It is the probability of rejecting the null hypothesis given that the null hypothesis is true.
  d) It is the value of the sample statistic.
  e) It is the absolute value of the difference between the parameter and the sample statistic.

16) Which of the following statements is true?
  a) If the null hypothesis is not rejected, there is strong statistical evidence that the null hypothesis is true.
  b) The choice of the alternative depends on the value of the sample statistic.
  c) If the null hypothesis is not rejected, there is strong statistical evidence that the alternative hypothesis
     is true.
  d) If the value of the test statistic leads to rejection of H 0, it is customary to say that the decision is
     statistically significant.
  e) The standard error is used in the calculation of the z-test statistic.

17) Students investigating the packaging of Ruffles Potato Chips, labeled 28.3 grams, randomly selected 6 bags
and found a mean weight of 28.1 grams with standard deviation of 0.4 grams. What is the test statistic for the
alternative hypothesis that the bags contain less than the labeled amount?
  a) t = -1.22         b) t = 1.22             c) z = -1.22           d) p = 0.1103         e) p = 0.1376

18) Insurance companies estimate that the average weight of cars currently used in the U. S. is 3000 pounds. A
random sample of 91 cars had a t-test statistic of -1.452. At  = 0.1, is this strong evidence that the mean
weight of cars is less than 3000 pounds?
  a) Yes, since you would reject the null hypothesis.
  b) No, since you would reject the null hypothesis.
  c) No, since you would fail to reject the null hypothesis.
  d) Yes, since you would fail to reject the null hypothesis.
  e) There is not enough information to answer this question.

19) Which of the following statements is true?
  a) Z-tests are considered robust inferential procedures.
  b) When performing a test of significance, you begin with the assumption that the null hypothesis is true.
  c) Hypothesis test are used to estimate an unknown parameter.
  d) Since t-tests are robust, outliers do not affect the test statistic.
  e) When performing a right-tail test, you double the probability in the upper tail to obtain the p-value.

20) Which of the following does not mean essentially the same as “reject H 0”?
  a) The results are statistically significant.
  b) The p-value is less than the level of significance.
  c) The difference between the observed statistic and the hypothesized parameter value is too large to be
     due to chance.
  d) If H0 is true, then the probability of obtaining sample results as extreme or more extreme than those
     observed is very small.
  e) The results are due to chance.

				
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