An experiment was conducted to compare the strength of shirts for two different brands. A random sample of twelve shirts of brand A and a random sample of ten shirts of brand B were tested. Brand A gave average strength of 85kg with a sample standard deviation of 4, while brand B gave an average of 81kg and standard deviation of 5. Can we conclude at the 0.05 level of significance that the strength of brand A exceeds that of brand B by more than 2kg? Assume the nonulation to be annroximately normal with equal variances
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- Two types of plastic are suitable for use by an electronics component manufacturer. The breaking strength of this plastic is important. It is known that the population standard deviation of breaking strength for the two types of plastic are equal and known to be 1.0 psi. A random sample of 10 type 1 plastic produced a mean breaking strength of 162.7 psi while a random sample of 12 type 2 plastic produced a mean breaking strength of155.4 psi. The company will not adopt plastic type 1 unless its mean breaking strength exceeds that of plastic type 2 by at least 10 psi. Based on the sample data obtained, should the company adopt plastic type 1? Perform a hypothesis test at the 5% level of significance.An engineer is comparing voltages for two types of batteries (K and Q) using a sample of 3939 type K batteries and a sample of 5757 type Q batteries. The mean voltage is measured as 8.558.55 for the type K batteries with a standard deviation of 0.6830.683, and the mean voltage is 8.828.82 for type Q batteries with a standard deviation of 0.7910.791. Conduct a hypothesis test for the conjecture that the mean voltage for these two types of batteries is different. Let μ1μ1 be the true mean voltage for type K batteries and μ2μ2 be the true mean voltage for type Q batteries. Use a 0.020.02 level of significance. Step 3 of 4 : Determine the decision rule for rejecting the null hypothesis H0H0. Round the numerical portion of your answer to two decimal placesA researcher claims that the stomachs of blue crabs from Location A contain more fish than the stomachs of blue crabs from Location B. The stomach contents of a sample of 17 blue crabs from Location A contain a mean of 197 milligrams of fish and a standard deviation of 39 milligrams. The stomach contents of a sample of 7 blue crabs from Location B contain a mean of 187 milligrams of fish and a standard deviation of 43 milligrams. At α=0.10 can you support the researcher's claim? Assume the population variances are equal. Complete parts (a) through (d) below. (a) Identify the null and alternative hypotheses. Choose the correct answer below. (b) Find the standardized test statistic for μ1−μ2. t= (Round to three decimal places as needed.) (c) Find the P Value
- An electrical engineer wishes to compare the mean lifetimes of two types of transistors in an application involving high-temperature performance. A sample of 60 transistors of type A were tested and were found to have a mean lifetime of 1827 hours and a standard deviation of 174 hours. A sample of 180 transistors of type B were tested and were found to have a mean lifetime of 1658 hours and a standard deviation of 231 hours. Let ux represent the population mean for transistors of type A and µy represent the population mean for transistors of type B. Find a 95% confidence interval for the difference uy – µy . Round the answers to three decimal places. The 95% confidence interval isA researcher claims that the stomachs of blue crabs from Location A contain more fish than the stomachs of blue crabs from Location B. The stomach contents of a sample of 13 blue crabs from Location A contain a mean of 191 milligrams of fish and a standard deviation of 37 milligrams. The stomach contents of a sample of 7 blue crabs from Location B contain a mean of 185 milligrams of fish and a standard deviation of 41 milligrams. At α=0.10, can you support the researcher's claim? Assume the population variances are equal and that both samples are from normal populations. Complete parts (a) through (d) below. (a) Identify the null and alternative hypotheses. Choose the correct answer below. A. H0: μ1−μ2=0 Ha: μ1−μ2>0 B. H0: μ1−μ2<0 Ha: μ1−μ2=0 C. H0: μ1−μ2=0 Ha: μ1−μ2≠0 D. H0: μ1−μ2=0 Ha: μ1−μ2<0 (b) Calculate the test statistic t=? (Round to three decimal places as needed.) (c) Calculate the…A researcher claims that the stomachs of blue crabs from Location A contain more fish than the stomachs of blue crabs from Location B. The stomach contents of a sample of 14 blue crabs from Location A contain a mean of 194 milligrams of fish and a standard deviation of 37 milligrams. The stomach contents of a sample of 8 blue crabs from Location B contain a mean of 184 milligrams of fish and a standard deviation of 44 milligrams. At a = 0.05, can you support the researcher's claim? Assume the population variances are equal. Complete parts (a) through (d) below. (a) Identify the null and alternative hypotheses. Choose the correct answer below. ОА. Но H1-H2 0 OD. Ho: H₁-12₂=0 Ha H1 H₂0 enough evidence at the 5% level of significance to support the researcher's claim.
- A researcher claims that the stomachs of blue crabs from Location A contain more fish than the stomachs of blue crabs from Location B. The stomach contents of a sample of 13 blue crabs from Location A contain a mean of 191 milligrams of fish and a standard deviation of 38 milligrams. The stomach contents of a sample of 8 blue crabs from Location B contain a mean of 189 milligrams of fish and a standard deviation of 44 milligrams. At a = 0.10, can you support the researcher's claim? Assume the population variances are equal. Complete parts (a) through (d) below. Ha: H1 - H2 = 0 Ha: H1 - H2 #0 (b) Find the standardized test statistic for µ1 -H2. t= (Round to three decimal places as needed.)A researcher claims that the stomachs of blue crabs from Location A contain more fish than the stomachs of blue crabs from Location B. The stomach contents of a sample of 13 blue crabs from Location A contain a mean of 191 milligrams of fish and a standard deviation of 38 milligrams. The stomach contents of a sample of 8 blue crabs from Location B contain a mean of 189 milligrams of fish and a standard deviation of 44 milligrams. At a = 0.10, can you support the researcher's claim? Assume the population variances are equal. Complete parts (a) through (d) below. t= 0.110 (Round to three decimal places as needed.) (c) Calculate the P-value. P=|| (Round to four decimal places as needed.)The burning rates of two different solid-fuel propellants used in air crew escape systems are being studied. A random sample of 15 first type propellants are tested resulting in a sample mean burning rate of 18 cm/s and sample standard deviation of 2.75 cm/s. Another sample of 15 second type propellants are tested resulting in a sample mean burning rate of 24 cm/s and sample standard deviation of 2.80 cm/s. Assume both populations are independent and normally distributed and have the equal but unknown variances. (a) Is there sufficient evidence to claim that the mean burning rate of the first type propellant is less than that of the second type propellant at α = 0.05? Use fixed significance level approach to answer this question. (b) Construct an appropriate confidence interval to answer question in part (a). (c) Without doing any calculation or looking up a table, can you figure out whether P-value is greater than 0.05? Why or why not?