Question

1. You are testing H0: µ = 0 against Ha: µ > 0 based on an SRS of 15 observations from a Normal population.

   • What values of the t statistic are statistically significant at the a = 0.005 level?

     1. t < - 3.326 or t > 3.326

     2. t > 2.977

     3. t < - 3.286 or t > 3.286

2. To study the metabolism of insects, researchers fed cockroaches measured amounts of a sugar solution. After 2, 5, and 10 hours, they dissected some of the cockroaches and measured the amount of sugar in various tissues. Five roaches fed the sugar D-glucose and dissected after 10 hours had the following amounts (in micrograms) of D-glucose in their hindguts - Amounts of D-glucose: 55.95 68.24 52.73 21.5 23.78

   • The researchers gave a 96% confidence interval for the mean amount of D-glucose in cockroach hindguts under these conditions. The insects are a random sample from a uniform population grown in the laboratory. We therefore expect responses to be Normal.

     1. The mean (±0.01) and the standard deviation (±0.0001) of the SRS are: x =_____   s = _________

     2. The critical value (±0.001) from the distribution for 96% confidence interval is: t*=______

     3. What confidence interval (±0.01) did the researchers give? _____ to _____

3. A study of commuting times reports the travel times to work of a random sample of 22 employed adults in Chicago. The mean is X= 28.28 minutes and the standard deviation is s = 17.2 minutes.

   • What is the standard error of the mean? _____

4. You are testing H0: µ = 100 against Ha: µ < 100 based on an SRS of 15 observations from a Normal population. The data give x⎯⎯⎯x¯ = 7 and = 4.7.

   • The value of the t statistic is _____

5. You are testing H0:μ=100 H0:μ=100 against Ha:μ<100 Ha:μ<100 with degrees of freedom of 24. The t statistic is 2.25

   • The P-value for the statistic falls between ____ and ____

6. You have an SRS of 14 observations from a Normally distributed population.

   • What critical value would you use to obtain a 99.5% confidence interval for the mean of the population? _____

7. The placebo effect is particularly strong in patients with Parkinson's disease. To understand the workings of the placebo effect, scientists measure activity at a key point in the brain when patients receive a placebo that they think is an active drug and also when no treatment is given. The same six patients are measured both with and without the placebo, at different times. The six differences (treatment minus control) had x⎯⎯⎯x¯ = -0.316 and s = 0.169.

   • The value of the t statistic is ______

   • Is there significant evidence of a difference between treatment and control?

     1. Yes

     2. No

8. Researchers claim that women speak significantly more words per day than men. One estimate is that a woman uses about 20,000 words per day while a man uses about 7,000. To investigate such claims, one study used a special device to record the conversations of male and female university students over a four- day period. From these recordings, the daily word count of the 20 men in the study was determined. Here are their daily word counts:                                                 

28410	10078	15931	21681	37778
10571	12875	11079	17801	13184
8921	6496	8158	7011	4435
10063	3989	12636	10964	5246

• • What value we should remove from observation for applying t procedures? ____

  • A 90% confidence interval for the mean number of words per day of men at this university is from ___ to ___ words

  • Is there evidence at the 10% level that mean number of words per day of men a this university differs from 10000?

    1. Yes

    2. No

• Cola makers test new recipes for loss of sweetness during storage. Trained tasters rate the sweetness before and after storage. Here are the sweetness losses (sweetness before storage minus sweetness after storage) found by 10 tasters for one new cola recipe:

2.1	0.5	0.6	1.8	-0.4
2.2	-1.1	1.1	1.1	2.4

• • Take the data from these 10 carefully tasters as an SRS from a large population of all trained tasters

  • Is there evidence at the 5% level that the cola lost sweetness? If the cola has not lost sweetness, the ratings after should be the same as before it was stored

  • The test statistic is t = _____

    1. Yes

    2. No

• There is evidence that cytotoxic T lymphocytes (T cells) participate in controlling tumor growth and that they can be harnessed to use the body's immune system to treat cancer. One study investigated the use of a T cell-engaging antibody, blinatumomab, to recruit T cells to control tumor growth. The data below are T cell counts (1000 per microliter) at baseline (beginning of the study) and after 20 days on blinatumomab for 6 subjects in the study. The difference (after 20 days minus baseline) is the response variable.

  Baseline:    0.04 0.02 0 0.02 0.36   0.24

After 20 days: 0 0.37 1.2   0.05 1.12 0.24

Difference: -0.04 0.35 1.2   0.03 0.76 0

• Do the data evidence at the 1% level that the mean count of T cells is higher after 20 days on blinatumomab?

• The test statistic is t = ____

  1. Yes

  2. No

Answer 1

1: Sample size: n=15

Degree of freedom: df=n-1=14

Test is right tailed so critical value of t for  a = 0.005 using excel function "=TINV(0.01,14)" is 2.977.

Rejection region:

If t > 2.977, reject H0

2:

Following is the output of descriptive statistics:

Descriptive statistics
	X
count	5
mean	44.4400
sample standard deviation	20.7408
sample variance	430.1809
minimum	21.5
maximum	68.24
range	46.74

The required confidence interval is (16.62, 72.56).