sample of 7 measurments, randomly selected from a normally distributed population, resulted in a sample mean, x¯=6.3 and sample standard deviation=1.07. Using α=0.01, test the null hypothesis that the mean of the
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A sample of 7 measurments, randomly selected from a
(a) the degree of freedom
(b) the critical ?t value
(c) the test statistic
The final conclustion is
A. We can reject the null hypothesis that μ=6.7 and accept that μ<6.7.
B. There is not sufficient evidence to reject the null hypothesis that μ=6.7.
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- A consumer group claims that the mean minimum time it takes for a sedan to travel a quarter mile is greater than 14.8 seconds. A random sample of 24 sedans has a mean minimum time to travel a quarter mile of 15.5 seconds and a standard deviation of 2.08 seconds. At α=0.10 is there enough evidence to support the consumer group's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. (a) Identify the claim and state H0 and Ha. H0: muμ ▼ enter your response here Ha: ▼ sigma squaredσ2 muμ sigmaσ pp ▼ not equals≠ greater than or equals≥ greater than> less than< less than or equals≤ equals= enter your response here (Type integers or decimals. Do not round.) The claim is the ▼ alternative null hypothesis.The desired percentage of SiO₂ in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO₂ in a sample is normally distributed with = 0.32 and that x = 5.23. (Use a = 0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5? State the appropriate null and alternative hypotheses. O Ho: μ = 5.5 H₂:μ> 5.5 O Ho: μ = 5.5 H₂: μ = 5.5 ⒸHO: μ = 5.5 H₂:μ ≥ 5.5 O Ho: μ = 5.5 H₂: μ< 5.5 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. O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true verage percentage differs from the desired percentage. O Reject the null hypothesis. There is not sufficient evidence to…Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P(Туре Freq. 11.15 A theory says that in a certain population, half the objects are of type A and the remainder are evenly divided among three types, B, C, and D. A random sample from the population breaks down as shown in the table at right. Does the data show 25 13 8. a statistically significant departure from what the theory predicts? Test using a = .05. ABCDSuppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) 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