Question

(20.44) 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 0.3 0.6 2.1 -0.4 2.2 -1.3 1.2 1.1 2.2

Take the data from these 10 carefully trained 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 statisic is t = ___ (±0.001)

No Yes .

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 0.31 0.29

After 20 days 0.18 0.27 1.2 0.05 1.02 0.34

Difference 0.14 0.25 1.2 0.03 0.71 0.05

Do the data give evidence at the 4 % level that the mean count of T cells is higher after 20 days on blinatumomab? The test statistic is

t =____ (±0.001)

Yes No

can you please show how to get the T on a TI-84.

Answer 1

Problem 1:

H0: Null Hypothesis: = 0 ( the cola has not lost sweetness )

HA: Alternative Hypothesis: 0 ( the cola has lost sweetness ) (Claim)

From the given d = sweetness before storage minus sweetness after storage values,the following statistics are calculated:

n = 10

= 1.0

sd = 1.2037

= 0.05

df = 10 - 1 = 9

To get critical value of t corresponding to = 0.05 and df = 9 in TI - 84 Calculator, the following steps are done:

Step 1: Press "2ND"

Step 2: Press "VARS"

Step 3: Choose: invTC

Step 4: Press "ENTER"

Step 5: Input are (i.e., Confidence level: 0.95)

Step 6: Input df (Value: 9)

Step 7: Press:ENTER,

we get:
Critical value of t = 2.262

Test Statistic is given by:

Since calculated value of t = 2.627 is greater than critical value of t = 2.262, the difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that the cola has lost sweetness .

So,

Answers to questions asked:

The test statistic t = 2.627

Yes

Problem 2:

H0: Null Hypothesis: 0 ( the mean count of T cells is not higher after 20 days on blinatumomab )

HA: Alternative Hypothesis: > 0 ( the mean count of T cells is higher after 20 days on blinatumomab) (Claim)

From the given d = Baeline - After ,the following statistics are calculated:

n = 6

= 0.3967

sd = 0.4659

= 0.04

df = 6 - 1 = 5

To get critical value of t corresponding to = 0.04 and df = 5 in TI - 84 Calculator, the following steps are done:

Step 1: Press "2ND"

Step 2: Press "VARS"

Step 3: Choose: invTC

Step 4: Press "ENTER"

Step 5: Input are (i.e., Confidence level: 0.96)

Step 6: Input df (Value: 5)

Step 7: Press:ENTER,

we get:
Critical value of t = 2.191

Test Statistic is given by:

Since calculated value of t = 2.086 is less than critical value of t = 2.191, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data do not support the claim that the mean count of T cells is higher after 20 days on blinatumomab.

So,

Answers to questions asked:

The test statistic t = 2.086

No