Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 18 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with σ = 0.30 gram.

(a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.)

(b) What conditions are necessary for your calculations? (Select all that apply.)

uniform distribution of weightsσ is unknownσ is knownn is largenormal distribution of weights

(c) Interpret your results in the context of this problem.

The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.The probability to the true average weight of Allen's hummingbirds is equal to the sample mean.    There is a 20% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.There is an 80% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.12 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)
hummingbirds

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

A random sample of 5400 permanent dwellings on an entire reservation showed that 1648 were traditional hogans.

(a) Let p be the proportion of all permanent dwellings on the entire reservation that are traditional hogans. Find a point estimate for p. (Round your answer to four decimal places.)


(b) Find a 99% confidence interval for p. (Round your answer to three decimal places.)

Give a brief interpretation of the confidence interval.

99% of all confidence intervals would include the true proportion of traditional hogans.

1% of all confidence intervals would include the true proportion of traditional hogans.     

99% of the confidence intervals created using this method would include the true proportion of traditional hogans.

1% of the confidence intervals created using this method would include the true proportion of traditional hogans.

(c) Do you think that np > 5 and nq > 5 are satisfied for this problem? Explain why this would be an important consideration.

Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.

No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.     

Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.

No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.

A courier service advertises that its average delivery time is less than 6 hours for local deliveries. A sample of 16 local deliveries was recorded and yielded the statistics     x =   5.83 hours and s = 1.59 hours. At the 5% significance level, conduct a hypothesis test to determine whether there is sufficient evidence to support the courier’s advertisement.  

Suppose the heights of 18-year-old men are approximately normally distributed, with mean 66 inches and standard deviation 6 inches.

(a) What is the probability that an 18-year-old man selected at random is between 65 and 67 inches tall? (Round your answer to four decimal places.)


(b) If a random sample of twenty-three 18-year-old men is selected, what is the probability that the mean height x is between 65 and 67 inches? (Round your answer to four decimal places.)


(c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?

The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.

The probability in part (b) is much higher because the mean is smaller for the x distribution.     

The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.

The probability in part (b) is much higher because the standard deviation is larger for the x distribution.

The probability in part (b) is much higher because the mean is larger for the x distribution.

1. Suppose we have the following values on the number of customers (X) and the average profits (Y) for fifteen stores:

Store                   Customers (X)            Average Profits (Y)

A                               161                              157

B                               99                              93

C                               135                              136

D                               120                              123

E                                164                              153

F                                221                              241

G                               179                              201

H                               204                              206

I                                 214                              229

J                                101                              135

K                               231                              224

L                                206                              195

M                               248                              242

N                               107                              115

O                               205                              197

Use the Spearman’s Rank Correlation test at the 0.05 level to see if X and Y are significantly related.

1. A store sells three different clothing designs and has recorded sales of each over five different 24-hour periods:

Design A         Design B            Design C

     16                    33                    23

     18                    31                    27

     19                    37                    21

     17                    29                    28

     13                    34                    25

Use the Kruskal-Wallis H test and the Chi-Square table at the 0.05 level to compare the three designs.

The following are quality control data for a manufacturing process at Kensprt Chemical Company. The data show the temperature in degrees centigrade at five points in time during the manufacturing cycle. The company is interested in using quality control charts in monitoring the temperature of its manufacturing cycle. Construct an X bar and R chart and indicate what its tells you about the process.

Sample      X bar      R

     1            95.72    1.0

     2            95.24      .9

     3            95.38      .8

     4            95.44      .4

     5            95.46      .5

     6            95.38    1.1

     7            95.40      .9

     8            95.44      .3

     9            95.08      .2

    10           95.50      .6

    11           95.80      .6

    12          95.22      .2

    13           95.56    1.3

    14           95.22      .5

    15           95.74      .8

    16          95.72     1.1

    17          94.82       .6

    18          95.46       .5

    19          95.60       .4

    20          95.64       .6

An airline operates a call center to handle customer questions and complaints. the airline monitors a sample of calls to help ensure that the service being offered is of high quality. The random samples of 100 calls each were monitored under normal conditions. The center can be thought of as being in control when these 10 samples were taken. The number of calls in each sample not resulting in a satisfactory resolution for the customer is as follows:

4 5 3 2 3 3 4 6 4 7

a. What is an estimate of the proportion of calls not resulting in a satisfactory outcome for the customer when the center is in control?

b. Construct the upper and lower limits for a p chart for the process.

c. With the results in part b. what is your conclusion if a sample of 100 calls has 12 calls not resulting in a satisfactory outcome for the customer?

A study was designed to compare the attitudes of two groups of nursing students towards computers. Group 1 had previously taken a statistical methods course that involved significant computer interaction. Group 2 had taken a statistic methods course that did not use computers. The students' attitudes were measured by administering the Computer Anxiety Rating Scale (CARS). A random sample of 10 nursing students from Group 1 resulted in a mean score of 65.8 with a standard deviation of 5.1. A random sample of 16 nursing students from Group 2 resulted in a mean score of 70.4 with a standard deviation of 7.6. Can you conclude that the mean score for Group 1 is significantly lower than the mean score for Group 2? Let μ1 represent the mean score for Group 1 and μ2 represent the mean score for Group 2. Use a significance level of α=0.05 for the test. Assume that the population variances are equal and that the two populations are normally distributed.

Step 1 of 4: State the null and alternative hypotheses for the test.

Step 2 of 4: Compute the value of the t test statistic. Round your answer to three decimal places.

Step 3 of 4: Determine the decision rule for rejecting the null hypothesis H0. Round your answer to three decimal places.

Step 4 of 4: State the test's conclusion.

1. A business consultant believes consumers equally prefer four brands of coffee (A, B, C, D). He collects a random sample of 400 consumers with the following results on preferences:

   Observed

   Frequency

Brand              of Preferences

               A                          102

               B                         121

               C                          120

               D                            57

Use an Excel spreadsheet to test this hypothesis at the 0.05 level. Submit the Excel spreadsheet you create along with an explanation of results

A certain drug is tested for its effect on blood pressure. Seven male patients have their systolic blood pressure measured before and after receiving the drug with the results shown below (in mm Hg).

                                    Patient                SBP before       SBP after

                                         1                          120                  125

                                         2                          124                  126

                                         3                          130                  138

                                         4                          118                  117

                                         5                          140                  143

                                         6                          128                  128

                                         7                          140                  146

a. (2) State, in prose, the study hypothesis (two-tailed).

b. (2) What test statistic(s) test would you use?

c. (2) What is the critical value of the test statistic?

d. (3) If the value of the test statistic is t = 2.67, what do you conclude (reject/do not reject is not sufficient).

partial credit, 12.1.11-T A manufacturer of colored candies states that 13​% of the candies in a bag should be​ brown, 14​% ​yellow, 13​% ​red, 24​% ​blue, 20​% ​orange, and 16​% green. A student randomly selected a bag of colored candies. He counted the number of candies of each color and obtained the results shown in the table. Test whether the bag of colored candies follows the distribution stated above at the alpha equals0.05 level of significance. Determine the null and alternative hypotheses. Choose the correct answer below. A. H0​: The distribution of colors is not the same as stated by the manufacturer. H1​: The distribution of colors is the same as stated by the manufacturer. B. H0​: The distribution of colors is the same as stated by the manufacturer. H1​: The distribution of colors is not the same as stated by the manufacturer. C. None of these. Click to select your answer and then click Check Answer. 4 parts remaining Observed Distribution of Colors Colored Candies in a bag Color Brown Yellow Red Blue Orange Green Frequency 61 64 52 63 96 66 Claimed Proportion 0.13 0.14 0.13 0.24 0.20 0.16 What is the test​ statistic? chi Subscript 0 Superscript 2 equals ​(Round to three decimal places as​ needed.) What is the​ P-value of the​ test? ​P-valueequals ​(Round to three decimal places as​ needed.) Based on the​ results, do the colors follow the same distribution as stated in the​ problem? A. Do not reject Upper H 0. There is sufficient evidence that the distribution of colors is not the same as stated by the manufacturer. B. Do not reject Upper H 0. There is not sufficient evidence that the distribution of colors is not the same as stated by the manufacturer. C. Reject Upper H 0. There is sufficient evidence that the distribution of colors is not the same as stated by the manufacturer. Your answer is correct.D. Reject Upper H 0. There is not sufficient evidence that the distribution of colors is not the same as stated by the manufacturer.

How do you perform Hypothesis Testing on a regression model using an ANOVA table below. This is to show the significance of the 4 independent variables.

1. Describe what qualitative forecasting models are. What are the advantages and disadvantages of this modelling?
2. “High correlation between two variables means that one is the cause and the other is the effect”. Explain this statement

Listed below are systolic blood pressure measurements​ (in mm​ Hg) obtained from the same woman. Find the regression​ equation, letting the right arm blood pressure be the predictor​ (x) variable. Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 100 mm Hg. Use a significance level of 0.05.

Right Arm

102

101

93

76

77

Left Arm

174

167

181

144

146