7.1-7.4
What is a point estimate?
A single number that is used to estimate the value of an unknown parameter.
Determine whether the outcome is a Type I error, a Type II error, or a correct decision.
The test is made of H0: μ = 45 versus H1: μ <45
The true value of μ is 44 and the H0 is not rejected.
What is the outcome of the test?
Type ll error
The test which is made of H0: μ = 2 versus H1: μ ≠ 2 is performed using a significance level of a= 0.05. The P value is 0.07.
Is the H0 rejected?
Do not reject.
A popular blog reports that 60% of college students log in to Facebook on a daily basis. The Dean of Students at a certain university thinks that the proportion may be different at her university. She polls a simple random sample of 200 students, and 135 of them report that they log in to Facebook daily. Can you conclude that the proportion of students who log in to Facebook daily is greater than 0.60?
H0: p = 0.60
H1: p > 0.60
Compute the p-value. Round your answer to three decimal places if needed.
Do you reject H0? Use the a=0.05 level.
0.015; yes
What is the margin of error?
Tells you how far off your estimate could be from the true value.
Determine whether the outcome is a Type I error, a Type II error, or a correct decision.
The test is made of H0: μ = 20 versus H1: μ ≠ 20
The true value of μ is 25 and the H0 is rejected.
What is the outcome of the test?
A study conducted by a technology company showed that the mean time spent per day browsing the video streaming service Netflix for something to watch was 20.6 minutes. Assume the standard deviation is σ=7. Suppose a simple random sample of 109 visits taken this year has a sample mean of x-bar= 21.6 minutes. A social scientist is interested to know whether the mean time browsing Netflix has increased. Use the a= 0.01 level of significance and the P-value method.
State the appropriate null and alternate hypotheses, p value, and the outcome of the test.
H0 = 20.6 H1 > 20.6 z = 1.49. P value = 0.0679. Do not reject the null
A poll surveyed 341 video gamers, and 95 of them said that they prefer playing games on a console, rather than a computer or hand-held device. An executive at a game console manufacturing company claims that the proportion of gamers who prefer consoles differs from 29%. Does the poll provide convincing evidence that the claim is true? Use the a= 0.05 level of significance and the p-value method with the TI-84 Plus calculator.
State the appropriate null and alternate hypothesis.
Compute the p-value. Round to 4 decimal places.
Do you reject H0? Use the a=0.01 level.
H0: p = 0.29 H1: p ≠ 0.29; 0.6425; Do not reject.
Find the critical value z a/2 needed to construct a confidence interval with level 86%. Round to 2 decimals.
1.48
In a recent year, the mean weight of newborn boys in a certain country was 7.5 pounds. A doctor wants to know whether the mean weight of newborn girls is lower than this. State the appropriate null and alternate hypotheses.
The null hypothesis is H0 μ: ? (=, >, <, ≠) __
The alternate hypothesis is H1 μ: ? (=, >, <, ≠) __
= 7.5, < 7.5
If H0 is rejected at the a= 0.05 level, which of the following is the best conclusion?
We cannot determine whether the H0 is rejected at the a= 0.10 level.
H0 is also rejected at the a= 0.10 level.
Ho is not rejected at the a= o.10 level.
B
The General Social Survey sampled 710 employed people and asked them how satisfied they were with their jobs. Of the 710 people sampled, 331 said that they were completely satisfied or very satisfied with their jobs. Can you conclude that the percentage of people who are completely or very satisfied with their jobs is greater than 0.45?
H0: p = 0.45
H1: p > 0.45
Compute the value of the test statistic. Round your answer to two decimal places.
Do you reject H0? Use the a=0.01 level.
0.87; no
Find the critical value z a/2 needed to construct a confidence interval with level 98%. Round to 2 decimals.
2.33
A computer magazine editor claims that the mean cost of a gaming computer is $1250. A test is made of H0 μ: = 1250 versus H1 μ: > 1250. The null hypothesis is rejected. State an appropriate conclusion.
There __enough evidence to conclude that the mean cost is __ $1250.
Is, more than >
The mean annual tuition and fees for a sample of 22 private colleges in California was $38,750 with a standard deviation of $7200. A dotplot shows that it is reasonable to assume that the population is approximately normal. Can you conclude that the mean tuition and fees for private institutions in California differs from $35000.Use the a = 0.01 level of significance and the P- value value method with the TI-84 Plus calculator.
State the appropriate null and alternate hypotheses, t, p value, and the outcome of the test.
H0 = 35000 H1 ≠ 35000. T = 2.44. P value = 0.0235. Do not reject the null.
In a simple random sample of 300 electronic components, 35 were defective. Can you conclude that more than 10% of components of this type are defective?
Find the p-value. Round to 4 decimal places.
What is the decision? Do you reject H0?
.1680, .9623, Do not reject.
Use the given data to construct a 99.5% confidence interval for the population proportion x = 52, n = 71, confidence level 99.5%. Round the answer to three decimal places.
(0.585, 0.880)
A wedding planner reports that the mean wedding cost is less than $28,000. test is made of H0 μ: = 28000 versus H1μ: < 28000. The null hypothesis is rejected. State an appropriate conclusion.
There __enough evidence to conclude that the mean cost is __ $28000.
Is, less than
A community survey sampled 1923 people in Colorado and asked them how long it took them to commute to work each day. The sample mean one-way commute time was 25.4 minutes with a standard deviation of 13 minutes. A transportation engineer claims that the mean commute time is greater than 25 minutes. Do the data provide convincing evidence that the engineer's claim is true? Use the a = 0.01 level of significance and the P- value value method with the TI-84 Plus calculator.
State the appropriate null and alternate hypotheses, t, p value, and the outcome of the test.
H0 = 25 H1 > 25. T = 1.35. P value = 0.0887. Do not reject the null.
A simple random sample of size 150 cars undergoing emissions testing, 23 failed the test. Can you conclude that the proportion of cars that fail the test is less than 20% at the a = 0.05 level of significance?
Find the p-value. Round to 4 decimal places.
What is the decision? Do you reject H0?
.0765; Do not reject.