Question

In: Statistics and Probability

A random sample of 145 recent donations at a certain blood bank reveals that 81 were...

A random sample of 145 recent donations at a certain blood bank reveals that 81 were type A blood. Does this suggest that the actual percentage of type A donations differs from 40%, the percentage of the population having type A blood? Carry out a test of the appropriate hypotheses using a significance level of 0.01.
State the appropriate null and alternative hypotheses.

H0: p = 0.40
Ha: p > 0.40 H0: p = 0.40
Ha: p < 0.40     H0: p = 0.40
Ha: p ≠ 0.40 H0: p ≠ 0.40
Ha: p = 0.40


Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)

z =
P-value =



State the conclusion in the problem context.

Reject the null hypothesis. There is not sufficient evidence to conclude that the percentage of type A donations differs from 40%. Do not reject the null hypothesis. There is sufficient evidence to conclude that the percentage of type A donations differs from 40%.     Reject the null hypothesis. There is sufficient evidence to conclude that the percentage of type A donations differs from 40%. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the percentage of type A donations differs from 40%.


Would your conclusion have been different if a significance level of 0.05 had been used?

Yes No    


You may need to use the appropriate table in the Appendix of Tables to answer this question.

Solutions

Expert Solution

Solution:

Here, we have to use one sample z test for the population proportion.

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H0: The actual percentage of type A donations not differs from 40%.

Alternative hypothesis: Ha: The actual percentage of type A donations differs from 40%.

H0: p = 0.40

Ha: p ≠ 0.40

This is a two tailed test.

We are given

Level of significance = α = 0.01

Test statistic formula for this test is given as below:

Z = (p̂ - p)/sqrt(pq/n)

Where, p̂ = Sample proportion, p is population proportion, q = 1 - p, and n is sample size

x = number of items of interest = 81

n = sample size = 145

p̂ = x/n = 81/145 = 0.55862069

p = 0.40

q = 1 - p = 0.60

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.55862069 – 0.40)/sqrt(0.40*0.60/145)

Z = 3.8989

Test statistic = Z = 3.90

P-value = 0.0001

(by using z-table)

P-value < α = 0.01

So, we reject the null hypothesis

There is sufficient evidence to conclude that the actual percentage of type A donations differs from 40%.

Reject the null hypothesis. There is sufficient evidence to conclude that the percentage of type A donations differs from 40%.

Would your conclusion have been different if a significance level of 0.05 had been used?

No

...because p-value is less than 0.05


Related Solutions

A random sample of 158 recent donations at a certain blood bank reveals that 86 were...
A random sample of 158 recent donations at a certain blood bank reveals that 86 were type A blood. Does this suggest that the actual percentage of type A donations differs from 40%, the percentage of the population having type A blood? Carry out a test of the appropriate hypotheses using a significance level of 0.01. State the appropriate null and alternative hypotheses. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and...
A random sample of 154 recent donations at a certain blood bank reveals that 84 were...
A random sample of 154 recent donations at a certain blood bank reveals that 84 were type A blood. Does this suggest that the actual percentage of type A donations differs from 40%, the percentage of the population having type A blood? Carry out a test of the appropriate hypotheses using a significance level of 0.01. State the appropriate null and alternative hypotheses. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and...
A random sample of 152 recent donations at a certain blood bank reveals that 88 were...
A random sample of 152 recent donations at a certain blood bank reveals that 88 were type A blood. Does this suggest that the actual percentage of type A donations differs from 40%, the percentage of the population having type A blood? Carry out a test of the appropriate hypotheses using a significance level of 0.01. State the appropriate null and alternative hypotheses. H0: p = 0.40 Ha: p > 0.40 H0: p = 0.40 Ha: p ≠ 0.40     H0:...
A random sample of 158 recent donations at a certain blood bank reveals that 88 were...
A random sample of 158 recent donations at a certain blood bank reveals that 88 were type A blood. Does this suggest that the actual percentage of type A donations differs from 40%, the percentage of the population having type A blood? Carry out a test of the appropriate hypotheses using a significance level of 0.01. State the appropriate null and alternative hypotheses. what is the z value? What is the p-value
A random sample of 81 lighting flashes in a certain region resulted in a sample average...
A random sample of 81 lighting flashes in a certain region resulted in a sample average radar echo duration of 0.8168 sec and a sample standard deviation of 0.36 sec (“Lighting Strikes to an Airplane in a Thunderstorm”, Journal of Aircraft, 1984). Calculate a 99% (two-sided) confidence interval for the true average echo duration μ.
A nonprofit organization appeals for donations by phoning or emailing recent college graduates. A random sample...
A nonprofit organization appeals for donations by phoning or emailing recent college graduates. A random sample of 300 graduates shows that 40% of the 150 who were contacted by telephone actually made contributions compared to only 30% of the 150 who received email requests. Calculate a 95% confidence interval for the difference in the proportions of graduates who may make donations if contacted by phone or by email. Give your answer to at least 4 decimal places. (,) Interpret the...
The mean diastolic blood pressure for a random sample of 100 people was 81 millimeters of...
The mean diastolic blood pressure for a random sample of 100 people was 81 millimeters of mercury. If the standard deviation of individual blood pressure readings is known to be 10 millimeters of mercury, find a 90% confidence interval for the true mean diastolic blood pressure of all people. Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. What is the lower limit of the 90% confidence...
On the island of Lilliput, a sample random sample of 500 people reveals that 450 of...
On the island of Lilliput, a sample random sample of 500 people reveals that 450 of them prefer to open their egg on the small end. On the island of Blefuscu, a sample random sample of 400 people reveals that 345 of them prefer to open their egg on the small end. Assuming that Lilliputians and Blefuscuans are equally likely to open their egg on the small end, what is the probability of selecting samples of these sizes with the...
A random sample is selected from a population with a μ = 145 and a standard...
A random sample is selected from a population with a μ = 145 and a standard deviation of σ = 18. Determine the mean and standard deviation of the sampling distribution (round to 3 decimal places). a. n = 14 Mean: Standard deviation: b. n = 26 Mean: Standard deviation: c. n = 37 Mean: Standard deviation: d. n = 56 Mean: Standard deviation: e. n = 115 Mean: Standard deviation:
A random sample of 100 voters found that 46% were going to vote for a certain...
A random sample of 100 voters found that 46% were going to vote for a certain candidate. Find the 90% confidence interval for the population proportion of voters who will vote for that candidate. A. 38.7% < p < 53.3% B. 37.8% < p < 54.2% C. 41.9% < p < 50.1% D. 39.6% < p < 52.4%
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT