Hypothesis



Joseph Adams

MMI 409 – Biostatistics Midterm

Spring Quarter

Northwestern University

1. Does the new experimental drug significantly affect heart rates?

Hypothesis

To investigate the effect of a new experimental drug on heart rates, a researcher randomly sampled 12 patients, and randomly assigned 6 patients to an experimental group and 6 patients to a placebo group. The drug therapy and placebo were administered. Two hours after the drug was administered, the number of beats per minute was recorded for each patient.

Null Hypothesis: Average Heartbeat of Placebo Group = Average Heartbeat of Experimental Drug Group.

Alternative Hypothesis: Average Heartbeat of Placebo Group ≠ Average Heartbeat of Experimental Drug Group.

Statistical Procedure, Tests and Assumptions

An Independent Sample T-Test is necessitated to test the null hypothesis since there are two independent observations.

Assumptions:

• Normally distributed population

• Independent observations

• Simple random sample taken from population

• Equality of variances between groups

Results

|Group Statistics |

| |

| |Levene's Test for Equality of Variances |t-test for Equality of Means |

| |

| |Mean |N |Std. Deviation |Std. Error Mean |

|Pair 1 |

| |Paired Differences |t |df |Sig. (2-tailed) |

| |

|Dependent Variable:Temp (in Celcius) |

|Source |

|Device |

|Dependent Variable:Temp (in Celcius) |

|Device |Mean |Std. Error |95% Confidence Interval |

| | | |Lower Bound |Upper Bound |

|Device 1 |31.430 |.102 |31.221 |31.639 |

|Device 2 |31.510 |.102 |31.301 |31.719 |

|Device 3 |31.360 |.102 |31.151 |31.569 |

|Device 4 |31.340 |.102 |31.131 |31.549 |

Significance of .64 > .05, therefore the Null Hypothesis is accepted.

Inference

There is no evidence to suggest that average temperature recorded by the four devices differ significantly in the population. (They report the same average temperature).

2. Do the data suggest that the additional operator has resulted in lower wait times for patients?

Hypothesis

Patients of a large community clinic with large call volumes on average experience a 94 second wait time before the call is answered. In an effort to decrease wait time for patients, the clinic hired an additional phone operator. Wait times were collected on ten randomly selected phone calls on the first day that the additional operator was used.

Null Hypothesis: Average wait time prior to additional operator = Average wait time utilizing additional operator.

Alternative Hypothesis: Average wait time prior to additional operator ≠ Average wait time utilizing additional operator.

Statistical Procedure, Tests and Assumptions

Since one sample is drawn from the population, the outcome variable of interest is continuous, and a specific mean is available to test our hypothesis against, a One Sample T-test is appropriate.

Assumption:

• One sample is drawn from a normally distributed population

• Simple random sample taken from population

Results

|One-Sample Statistics |

| |N |Mean |Std. Deviation |Std. Error Mean |

|Wait Time in seconds |10 |79.1000 |32.53869 |10.28964 |

|One-Sample Test |

| |Test Value = 94 |

| |

|Dependent Variable:Weight (ounces) |

|Group |Mean |Std. Deviation |N |

|Breastfed |115.80 |3.899 |5 |

|Fed Formula A |104.40 |6.580 |5 |

|Fed Formula B |102.80 |5.119 |5 |

|Fed Formula C |103.60 |7.266 |5 |

|Total |106.65 |7.659 |20 |

|Tests of Between-Subjects Effects |

|Dependent Variable:Weight (ounces) |

|Source |

Significance of .009 < .05, therefore the Null Hypothesis is rejected.

|Multiple Comparisons |

|Weight (ounces) |

|Tukey HSD |

|(I) Group |

|*. The mean difference is significant at the |

|Weight (ounces) |

|Tukey HSDa,b |

|Group |N |Subset |

| | |1 |2 |

|Fed Formula B |5 |102.80 | |

|Fed Formula C |5 |103.60 | |

|Fed Formula A |5 |104.40 | |

|Breastfed |5 | |115.80 |

|Sig. | |.972 |1.000 |

|Means for groups in homogeneous subsets are displayed. |

|Based on observed means. |

|The error term is Mean Square(Error) = 34.375. |

|a. Uses Harmonic Mean Sample Size = 5.000. |

|b. Alpha = |

The average breastfed baby weight differs significantly from the Formula fed averages.

Inference

There is compelling evidence to suggest that the average weight differs significantly within the population between exclusively breastfed babies and exclusively formula fed babies. (Exclusively breastfed babies have a higher average weight.) There is no evidence to suggest that the average weights differ significantly amongst the formula fed populations.

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