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The life in hours of an electronic sensor is known to be approximately Normally distributed
$3.00$2.00Question:
The life in hours of an electronic sensor is known to be approximately Normally distributed, with population standard deviation = hours. A random sample of 10 sensors resulted in the following data: 500,550,560,575,525,505,510,540,550,545.
 Is there evidence to support the claim that mean life exceeds 520 hours? Use a fixedlevel test with alpha = 0.05.
 What is the Pvalue of this test? Conclude the same of part (a)?
 What is the Betavalue for this test if the true mean life is 535 hours?
 What sample size would be required to ensure that Beta does not exceed 0.10 if the true mean life is 540 hours?
 Construct a 95% onesided lower CI on the mean life.
 Use the CI found in part e) to test the hypothesis.

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A random sample of the number of farms (in thousands) in various states follows. Estimate the mean number of farms per state with 90 % confidence
$2.00$1.00Question:
A random sample of the number of farms (in thousands) in various states follows. Estimate the mean number of farms per state with 90 % confidence.
a) Assume population standard deviation is known and is equal to 31.
b) Assume that population standard deviation is not known.
47 95 54 33 64 48 57 9 80 8 90 3 49 4 44 79 80 48 16 68 7 15 21 52 6 78 109 40 50 29 5.

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A different sample of size n = 20 produced a sample mean of 31.08% and a sample standard deviation of 5.48%.
$2.00$1.00Question:
A different sample of size n = 20 produced a sample mean of 31.08% and a sample standard deviation of 5.48%. Use these values to calculate a 90% confidence interval for the national mean percent of lowincome working families. Please show all calculations and provide the upper and lower limits that make up the confidence interval. (Round the limits to two decimal places).