Of a random sample of 69 health insurance firms, 47 did public relations in-house, as did 40 of an independent random sample of 69 casualty insurance firms. Find and interpret the p-value of a test of equality of the population proportions against a two-sided alternative.
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Of a random sample of 69 health insurance firms, 47 did public relations in-house, as did 40 of an independent random sample of 69 casualty insurance firms. Find and interpret the p-value of a test of equality of the population proportions against a two-sided alternative.
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- A direct mail appeal for contributions from a university’s alumni and supporters is considered to be too costly if less than 15% of the alumni and supporters provide monetary contributions. To determine if a direct mail appeal is cost effective, the fundraising director sends the direct mail brochures to a simple random sample of 173 people on the alumni and supporters mailing lists. They receive monetary contributions from 18 people. Does this evidence demonstrate that the direct mail campaign is not cost effective? Use a 0.02 level of significance. Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below. H0: p=0.15 Ha: p⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯0.15A direct mail appeal for contributions from a university’s alumni and supporters is considered to be too costly if less than 14% of the alumni and supporters provide monetary contributions. To determine if a direct mail appeal is cost effective, the fundraising director sends the direct mail brochures to a simple random sample of 206 people on the alumni and supporters mailing lists. They receive monetary contributions from 21 people. Does this evidence demonstrate that the direct mail campaign is not cost effective? Use a 0.10 level of significance.Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places.A company that produces a particular brand of juice knows that about 30% of people select that brand if given a choice of all brands. To determine if a commercial would be an effective advertising tool, the company invites 100 people to view a 30-minute program that includes a commercial for the company’s juice. After the program, the participants are offered a choice of juice brands. In this trial, 36 of the 100 participants chose the company’s juice. When a significance test was performed to determine if the true proportion of people who watch the commercial and select the company’s juice exceeds 30%, the P-value was 0.0952. At the α = 0.05 significance level, what decision should the company make? A. Because the P-value of 0.0952 > α = 0.05, the company has evidence that the true proportion of those who would select the company’s juice is larger than 30%. B. Because the P-value of 0.0952 < 0.3, the company has evidence that the true proportion of those who would select the…
- The General Social Survey is an annual survey given to about 1500 U.S. adults selected at random. A recent survey contained the question "How important to your life is having a fulfilling job?" Of the 265 college graduates surveyed, 99 chose the response "Very important." Of the 118 people surveyed whose highest level of education was high school or less, 42 chose the response "Very important." Based on these data, can we conclude, at the 0.01 level of significance, that there is a difference between the proportion p₁ of all U.S. college graduates who would answer "Very important" and the proportion p of all U.S. adults whose highest level of education was high school or less who would answer "Very important"? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the parts below. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative…A shopkeeper wonders if number of their female and male customers are equal or not. They count the customers of each gender for a day, they find that 48 females and 53 males visit the shop. Make a hypothesis test to decide if number of females and males are significantly different from each other or not. Report a p-value for significance.In the Texas senate races, a candidate must clear 50% to avoid a runoff election. In a recent poll of 1040 voters in Texas, 51% of voters preferred candidate. We will a hypothesis test to see if we can say at the 5% significance level that more than 50% of voters in Texas prefer candidate based on this poll. State the null and alternative hypothesis. Find the test-statistic. Find the P-value. Make a conclusion. Interpret your answer.
- An LED light bulb manufacturer claims that the average lifespan of its 60-watt LED light bulbs is 27,000 hours. A corporate watchdog group is suspicious of the company's claim and thinks that the true average lifespan of the 60- watt LED light bulbs produced by the company may be less than the advertised 27,000 hours. The group collected and tested a random sample of 211 light bulbs and found the average lifespan of the sample was 26,941 hours. Use the p-value method to test the hypothesis that the mean lifespan of this brand of 60-watt LED light bulb is less than 27,000 hours, using a = 0.1. Assume the standard deviation of the lifespan of all such light bulbs is known to be 370 hours. State the null and alternative hypothesis for this test. Ho: ? H₁: ? Determine if this test is left-tailed, right-tailed, or two- tailed. right-tailed two-tailed left-tailed Should the standard normal (z) distribution or Student's (t) distribution be used for this test? The Student's t distribution…Among a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 159 said they decided not to go to college because they could not afford school. A. Calculate the test statistic and the p-value. B. State the conclusion in context.A direct mail appeal for contributions from a university’s alumni and supporters is considered to be too costly if less than 15% of the alumni and supporters provide monetary contributions. To determine if a direct mail appeal is cost effective, the fundraising director sends the direct mail brochures to a simple random sample of 173 people on the alumni and supporters mailing lists. They receive monetary contributions from 18 people. Does this evidence demonstrate that the direct mail campaign is not cost effective? Use a 0.02 level of significance. Step 3 of 3 : Draw a conclusion and interpret the decision. 1. We reject the null hypothesis and conclude that there is insufficient evidence at a 0.02 level of significance that the direct mail campaign is not cost effective. 2. We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.02 level of significance that the direct mail campaign is not cost effective. 3. We reject the null…