Two random samples (n=8) are selected from each of two packaging methods and the times for completion are given in the table below.

Method 1	85	83	92	68	82	81	82	78
Method 2	84	90	98	96	91	93	89	84

Experiment 3: Conduct a hypothesis test to test the claim that the time needed for packaging using method 1 is significantly differentfrom 90 seconds.

1. Let =

H_O:

H_a:

1. Calculate the test statistic for the third experiment:

• Click on cell I2. Type =average(C2:C9). This calculates the sample mean of the third experiment. Record this value rounded to the three places x-bar = __________.

• Click on cell I3. Type=stdev(C2:C9). This calculates the sample standard deviation of the third experiment. Record this value rounded to three places s = ________.

• Next, click on cell I4 and enter the formula =I3/SQRT(COUNT(C2:C9)). This value is the standard deviation of the sample means (this is called the standard error of the mean), and can be calculated by hand using formula . Record this value rounded to three places SE = _________.

• Click on the cell I5. Then click Formulas More Functions Statistical Standardize. A menu called Function Argumentsshould appear.
  • X is the value you want to standardize. This is the sample mean. Enter I2.
  • Mean is the mean of the sampling distribution. This is the hypothesized mean from your hypotheses in part a.
  • Standard deviation is the standard deviation of the sample means (standard error). Enter I4.

• Record the Test Statistic from cell I5. t_stat = ___________.

1. Calculate the p-value:

• Click on the cell I7. Then click Formulas More Functions Statistical T.Dist.2T. This function is calculating the p-value for a two-tailed t-test. A menu called Function Argumentsshould appear.
  • Xis the Test Statisticcalculated in part b.Enter this value from cell I5. (Note: If the test statistic is negative, change the sign to a positive when entering the test statistic for X).
  • Deg_freedomis the degrees of freedom. Recall df = n-1.

• Record the p-value from cell I7: p-value = .

1. Use the p-value and a .12 level of significance to determine if you should reject or not reject the null hypothesis. Hint: Reject H_o only if p-value
2. Use the p-value and a .02 level of significance to determine if you should reject or fail to reject the null hypothesis. Interpret in context.

data:

call time	calculator	method 1	method 2			Experiment 1	Experiment 2	Experiment 3	Experiment 4
24	298	85	84		Mean
18	295	83	90		Standard Deviation
16	303	92	98		Standard Error
28	292	68	96		Test Statistics
10	292	82	91		Critical value
12	301	81	93		p-value
20		82	89
18		78	84
24
17
6
14
18
26
14
20
8
6
10
10
24
25
14
24
22
16
18
16
20
22