# Project #33630 - Statistics

A systems analyst tests a new algorithm designed to work faster than the currently used algorithm. Each algorithm is applied to a group of 59 sample problems. The new algorithm completes the sample problems with a mean time of 19.46 hours and a standard deviation of 4.748 hours. The current algorithm completes the sample problems with a mean time of 21.91 hours and a standard deviation of 5.290 hours. Conduct a hypothesis test of conjecture that the new algoithm has a lower true mean completion time than the current algorithm. Let u1 be the true mean completion time for the new algorithm and u2 be the true mean completion time for the current algorithm. Use a significance level of a=0.01 for the test.  State the null and alternative hypotheses for the test. Compute the value of the z statistic.  Determine the decision rule for rejecting the null hypothesis.  State the test's conclusion.

A lumber company is making boards that are 2972.0 millimeters tall.  If the boards are too long they must be trimmed, and if they are too short they cannot be used. A sample of 25 boards is made, and it is found that they have a mean of 2973.8 millimeters with a variance of 225.00.  Is there evidence at the 0.025 level that the boards are too long and need to be trimmed?  Assume the population distribution is approximately normal.  Enter the value of the test statistic.  Specify if the test is one-tailed or two-tailed.  Enter the decision rule to reject H0 if t> ? Enter whether to reject null hypothesis or failed to reject null hypothesis.  A newspaper publisher believes that 69% of their readership own a Rolls Royce.  A random sample of 240 found that 65% of the readers owned a Rolls Royce.  Use a 0.05 level of significance.  Find the value of the test statistic.

Consider the relationship between the number of bids an item on eBay received and the item's selling price.  The following is a sample of 5 items sold through an auction.

PRICE IN DOLLARS| 27 | 32 | 46 | 48 | 49 |

NUMBER OF BIDS  |  2  | 4   | 7   | 8  |  9  |

Enter the sum of squared errors.  Use the values of b0 = -5.4413 and b1 = 0.2832 for the calculations.  Enter the estimated variance of errors.  Enter the estimated variance of slope. Construct the 90% C.I. for the slope and find the lower and upper bound. Construct the 98% C.I. for the slope and find the lower and upper bound.

A pharm company claims its new drug reducts systolic blood pressure.  The systolic blood pressure for 9 patients before taking the new drug and 2 hours after taking the drug are shown in the table below.  Is there enough evidence to support the company's claim?  Let d = blood pressure before taking new drug - blood pressure after taking new drug.  Use a significance level of a = 0.05 for the test.

PATIENT                             |  1  |  2  |  3  |  4  |  5  |  6  |   7  |  8  |  9  |

BLOOD PRESSURE BEFORE  | 185|162|198|164 |195 |183 |175 |174|164|

BLOOD PRESSURE AFTER     |169|155|192 |141|171 |160 |156 |153 |155|

State the null and alternative hypotheses.  Find the value of the standard deviation of the paired differences.  Compute the value of the t statistic.  Determine the decision rule for rejecting the null hypothesis.  State whether to reject null hypothesis or fail to reject null hypothesis.

The director of research and development is testing a new medicine.  She wants to know if there is evidence at the 0.05 level that the medicine relieves pain in more than 360 seconds.  For a sample of 88 patients, the mean time in which the medicine relieved pain was 365 seconds.  Assume a population variance of 400.  Enter the hypotheses H0 and Ha.  Enter the value of the test statistic.  Specify if the test is one tailed or two tailed.  Enter the P value of the test statistic.  Enter the value of the level of significance.  Enter whether to reject null hypothesis or failed to reject null hypothesis.

Colonial Funds claims to have a bond fund which has maintained a mean share price of \$15.  They claim that the variance of the share price is 0.11.  To test this claim, the investor randomly selects 19 days during the last year.  He finds an average share price of \$14.8- with a standard deviation of 0.5877.  Can the investor conclude that the share price of the bond fund varies by more than Colonial Funds claims at a=0.005? Enter the hypotheses in terms of the standard deviation.  Enter the critical value of the test statistic.  If the test is two tailed, separate the values with a comma.  Enter the value of the test statistic.  Should you reject the null hypothesis or fail to reject the null hypothesis. What is the conclusion - there is is sufficient evidence to show the share price varies by more than Colonial Funds claims or there is not sufficient evidence?

A drug, which is used for treating cancer, has potentially dangerous side effects if it is taken in doses which are larger than 53.41mg, the required dosage for the treatment.  It is important that the variance of the amount of the active ingredient is 0.02.  12 tablets are randomly selected and the amount of the drug in each tablet is measured.  It is determined that the variance of the amount of active ingredient is 0.0442mg.  Does the data suggect at a = 0.05 that the variance of the drug in the tablets is more than the desired amount? State the null and alternative hypotheses.  Enter the critical value of the test statistic.  Enter the value of the test statistic.  Should you reject the null hypothesis or fail to reject the null hypothesis?  Is there sufficient evidence to show that the amount of the active ingredient has a variance that is more than the desired amount?

A highway department executive claims that the number of fatal accidents which occur in her state does not vary from month to month.  The results of the survey of 132 fatal accidents were recorded.  Is there enough evidence to reject the executive's claim at a = 0.01?

MONTH  |  JAN  |  FEB  |  MAR  |  APRIL | MAY  | JUNE | JULY | AUG | SEP | OCT | NOV | DEC |

#        |  8      |   7     |  13    |   16     |  12    |   13  |  14   |  14   |  7    |  8    |  12   |  8    |

Indicate the correct formulation of the hypotheses:  H0: number of fatal accidents does vary from month to month Ha: number of fatal accidents does not vary from month to month OR H0: number of fatal accidents does not vary from month to month Ha: number of fatal accidents does vary from month to month.  Do all or some of the categories hypothesized have different probabilities?  Indicate the hypotheses formulated in Step 1 imply.  H0: all pi = ______  Ha: at least one pi does not equal _______. Enter the expected number of observations for JAN and APRIL.  Enter the value of the test statistic.  Enter the degrees of freedome associated with the test statistic.  Enter the critical value of the test statistic.  At the 0.01 level of significance, determine whether to fail or reject null hypothesis.  Is there sufficient evidence to reject the executive's claim?

The follow data gives the number of hours 7 students spent studying and their corresponding grades:

HOURS SPENT  |  0  |  1  |  2  |  3.5  |  4.5  |  5.5  |  6   |

GRADE            |  60 | 69 | 75 |   78  |  84    |  90  | 96  |

Calculate the correlation coefficient r to six decimal places.  Determine if r is statistically significant at the 0.05 level.  Calculate the coefficient of determination r^2 to three decimal places.

The following table compares the completion percentage and interception percentage of 5 NFL quarterbacks.

COMPLETION  |  55 | 56 | 56.5 | 58 | 59 |

INTERCEPTION| 4,5 | 4  |  3.5  | 2.5 | 2  |

Draw a scatter plot of the given data.  Estimate the correlation in words:  positive, negative, or no correlation. Calculate the coefficient r rounded to three decimal places.

Consider the following table:

___________________|        SS      |       DF        |        MS        |     F      |

AMOUNT TREATMENTS  |                  |      6           |      593.13    |             |

ERROR                         |                  |                   |      205.91    |             |

TOTAL                          |  5823.79    |       17        |                    |             |

Calculate the sum of squares among treatments rounded to two decimal places.  Calculate the sum of squares of experimental error to two decimal places.  Calculate the degrees of freedom of experiemental error.  Calculate the F-value to two decimal places.  What is the sum of squares of sample means about the grand mean to two decimal places? What is the variation of the individual measurements about their respective mean to two decimal places? What is the critical value of F at the level 0.1? Is F significant at 0.1?

The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions.  Using the date consider the equation of the regression line for predicting the number of bids an item will receive based on the list price.

PRICE IN DOLLARS |  109 |  111 | 116 | 151 | 156 |

NUMBER OF BIDS   |   11  |  12   |  13  |  17 |   19 |

Enter the estimated slope to three decimal places.  Enter the y-intercept to three decimal places.  Is it true or false that not all points predicted by the linear model fall on the same line?  Determine the value of the dependent variable y at x = 0.  Enter the estimated value of y when x = 151 to three decimal places.  Enter the value of the coefficient of determination to three decimal places.

Given two independent random samples with the following results:

n1 = 617       x1 = 167

n2 = 398       x2 = 151

Can it be concluded that there is a difference between the two population proportions?  Use a significance level of 0.02 for the test.  State the null and alternative hypotheses.  Find the values of the two sample proportions p1 and p2 to 3 decimal places.  Compute the weighted estimate of p, p to three decimal places.  Compute the value of the z test.  Determine the decision rule to reject the null hypothesis to two decimal places.  State whether to reject or failed to reject null hypothesis.

A standardized test is given to a 9th grade class and 10th grade class.  The superintendent believes that the variance in performance from the 9th grade class is smaller than 10th grade.  The sample variance of a sample of 19 test scores from 9th grade is 6.15.  The sample variance of 18 test scores from 10th grade is 16.98.  Test the claim using a 0.005 level of significance.  State the null and alternative hypotheses.  Determine the critical value of test statistic to four decimal places.  Compute value of test statistic.  Reject or fail to reject null hypothesis?  Does the evidence support the claim?

A student researcher compares the ages of cars owned by students and cars owned by faculty at college.  A sample of 271 cars owned by students had an average age of 8.78 years with a standard deviation of 2.32 years.  A sample of 238 cars owned by faculty had average age of 7.98 years with a standard deviation of 3.80 years.  Determine the 95% confidence interval for the difference between the true mean ages for cars owned by students and faculty.  Find the value of z alpha/2 to be used in confidence interval.  What is the upper and lower limit of the 95% confidence interval to two decimal points?

The following table was generated from the sample of 10 junior high students regarding the number of hours they are unsupervised per night, the average number of hours they play video games per night, and their final grades.

____________________________| COEFFICIENTS    |  STANDARD ERROR |  T STAT     |  P-VALUE   |

INTERCEPT                                  |  99.731709         |  6.598650               | 15.113956| 0.000005   |

HOURS UNSUPERVISED                |  1.899257           |  1.425202               | 1.332623  | 0.231029   |

HOURS PLAYING GAMES               |  -6.959950         |  1.655935               |  -4.203033| 0.005667    |

Write the multiple regression equation for the computer output given to three decimal places. Mark which independent variables, x1 or x2, could be eliminated if the level of significance is 0.01 or say "keep all variables" if none can be eliminated.

 Subject Mathematics Due By (Pacific Time) 06/20/2014 08:00 pm
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