Question

Dr. Hector claims that the mean birth weight of babies born at the hospital where he works is 8 pounds. Sheila, a nurse who assists Dr. Hector, wants to test this claim, so she takes a random sample of 55 babies born at the hospital. The following is the data from this study:

• The alternative hypothesis Ha:μ≠8.
• The sample mean weight of the 55 babies is 7.8 pounds.
• The sample standard deviation is 0.9 pounds.
• The test statistic is calculated as −1.65.

Using the information above and the portion of the t− table below, choose the correct p− value and interpretation for this hypothesis test.

Values for right-tail areas under the t-distribution curve

Probability	0.10	0.05	0.025	0.01	0.005
Degrees of Freedom
50	1.299	1.676	2.009	2.403	2.678
51	1.298	1.675	2.008	2.402	2.676
52	1.298	1.675	2.007	2.400	2.674
53	1.298	1.674	2.006	2.399	2.672
54	1.297	1.674	2.005	2.397	2.670
55	1.297	1.673	2.004	2.396	2.668
56	1.297	1.673	2.003	2.395	2.667
57	1.297	1.672	2.002	2.394	2.665
58	1.296	1.672	2.002	2.392	2.663
59	1.296	1.671	2.001	2.391	2.662

Select the correct answer below:

The probability of observing a value of t0=1.65 or more if the null hypothesis is true is between 0.05 and 0.20.

The probability of observing a value of t0=−1.65 or less or observing a value of t0=1.65 or more if the null hypothesis is true is between 0.10 and 0.20.

The probability of observing a value of t0=−1.65 or less or observing a value of t0=1.65 or more if the null hypothesis is true is between 0.01 and 0.02.

The probability of observing a value of t0=−1.65 or less if the null hypothesis is true is between 0.005 and 0.01.

Answer 1

from above degree of freedom =n-1=54

for 54 df to=1.65 falls between 1.297 and 1.674 for which corresponding probability is 0.10 and 0.05

since it is two tailed test , p value will be between 2*0.05 and 2*0.10 or between 0.10 and 0.20

Correct option is:

The probability of observing a value of t0=−1.65 or less or observing a value of t0=1.65 or more if the null hypothesis is true is between 0.10 and 0.20.