ACTIVITY A. Compute the z for each given claim (po), observed proportion (p ) and the sample size (n). 1. po= 10%, þ= .30, n = 100 2. po= 0.12, p= 0.32, n= 248 3. Po= 20%, p = .58, n = 312
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- The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the conditional probability of the event E, getting a six, given that the event F, getting an even number, has occurred is P(EF)=___________.An SRS of 100 flights by Speedy Airlines showed that 64 were on time. An SRS of 100 flights by Happy Airlines showed that 80 were on time. Let pS be the proportion of on-time flights for all Speedy Airline flights, and let pH be the proportion of all on-time flights for all Happy Airlines flights. Is there evidence of a difference in the on-time rate for the two airlines? To determine this, you test the hypotheses H0 : pS – pH 0, Ha : pS – pH 0. The P-value of your test is 0.0117. Which of the following is an appropriate interpretation of the P-value? a. If the on-time rates for the two airlines are equal, there is a 0.0117 probability of getting samples with a difference as far or farther from zero as these samples. b. If the on-time rates for the two airlines are not equal, the probability of getting samples with a difference as far or farther from zero as these samples is 0.9883. c. The probability of making a Type I error is 0.0117. d. The probability of making a Type II error…A new insecticide is advertised to kill more than 95% roaches upon contact. In a laboratory test, the insecticide was applied to 400 roaches and 384 died immediately after contact. Is this sufficient evidence to support the advertised claim? Use α{=0.05. (d) Conclusion for the problem above is
- Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 149 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. P-value?Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 150 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. a) State the appropriate null and alternate hypotheses. b) Find the P-value. c) Should a change be made?A sample of n= 64 scores has a mean of M= 68. Assuming that the population mean is u=60, find the z-score for this sample: If it was obtained from a population with o= 16 Z=
- A toy store chain claims that at least 80% of girls under 8 years old prefer dolls over other types of toys. After observing the buying pattern of many girls under 8 years old, we feel that this claim is inflated. In an attempt to dispose of this claim, we observe the buying pattern of 20 randomly selected girls under 8 years old, and we observe X, the number of girls who buy stuffed toys or dolls. We wish to test the hypothesis Ho : p = 0.8 against Ha : p < 0.8. Suppose we decide to accept the Ho if X > 12 (that is X ≥ 13). This means that if {X ≤ 12} (that is X < 13) we will reject Ho. (a) Find α(Type I error). (b) Find β(Type II error) for p = 0.6. (c) Find β for p = 0.4.(d) Find the rejection region of the form {X ≤ K} so that (i) α = 0.01; (ii) α = 0.05.(e) For the alternative Ha: p = 0.6, find β for the values of α in part (d).Suppose that Fred, a United States politician from a large western state, wants to create a new law that would require children under the age of 16 to be accompanied by an adult at all times in public places. Based on previous voting records, Fred believes that he could gain the support of 2525% of likely voters. To test his hypothesis, Fred conducts a random survey of 12001200 likely voters and asks if they would support his proposition. Let ?X denote the number of likely voters in Fred's sample that pledge their support, assuming that Fred's belief that 25%25% of likely voters would support his proposal. Which of the following statements are true about the sampling distribution of ?X? -The sampling distribution of ?X is approximately binomial with ?=1200n=1200 and ?=0.25p=0.25. -The sampling distribution of ?X is exactly normal with ?=0.5μ=0.5 and ?=0.0125σ=0.0125. -The sampling distribution of ?X is exactly binomial with ?=1200n=1200 and ?=0.25p=0.25. -The sampling…Assume that σ12 = σ22 = σ2. Calculate the pooled estimator of σ2 for s12=50, s22=57 and n1 =n2 =18.
- 9. A research center claims that 24% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 700 adults in that country, 28% say that they would travel into space on a commercial flight if they could afford it. At α=0.05, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below. Question content area bottom Part 1 (a) Identify the claim and state H0 and Ha. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. The percentage adults in the country who would travel into space on a commercial flight if they could afford it is not enter your response here %. B. No more than enter your response here % of adults in the country would travel into space on a commercial flight if they could afford it. C. At least…To increase egg production, a farmer decided to increase the number of times the lights in his henhouse were on. Ten hens were randomly selected, and the number of eggs each produced was recorded. After one week of lengthened light time, the same hens were monitored again. The data is given here. At α = 0.05, can it be concluded that the increased light time increased egg production? Hen 1 2 3 4 5 6 7 8 9 10 Before 4 3 8 7 6 4 9 7 6 5 After 6 5 9 7 4 5 10 6 9 6A sample is selected from a population with μ = 50 and σ = 12. If the sample mean of M = 56 produces a z-score of z = +1.00, then how many scores are in the sample?