Math

1.A simple random sample of45 men from a normally distributed population results in a standard deviation of11.3 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normalrange, the result is a standard deviation of10 beats per minute. Use the sample results with a0.05 significance level to test the claim that pulse rates of men have a standard deviation equal to10 beats per minute. Complete parts(a) through(d) below.

Calculate the value of the test statistic,

i) 2= -------

ii) P=--------

1a. The piston diameter of a certain hand pump is0.8 inch. The manager determines that the diameters are normallydistributed, with a mean of0.8 inch and a standard deviation of0.006 inch. After recalibrating the productionmachine, the manager randomly selects23 pistons and determines that the standard deviation is0.0044 inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at the=0.05 level ofsignificance?

Calculate the value of the test statistic.

2=

P- value=

b). Suppose a mutual fund qualifies as having moderate risk if the standard deviation of its monthly rate of return is less than5%. Amutual-fund rating agency randomly selects21 months and determines the rate of return for a certain fund. The standard deviation of the rate of return is computed to be3.72%. Is there sufficient evidence to conclude that the fund has moderate risk at the=0.10 level ofsignificance? A normal probability plot indicates that the monthly rates of return are normally distributed.

Calculate the value of the test statistic,

i) 2= -------

ii) P=--------

c). Workers at a certain soda drink factory collected data on the volumes(in ounces) of a simple random sample of17 cans of the soda drink. Those volumes have a mean of 12.19 oz and a standard deviation of0.12 oz, and they appear to be from a normally distributed population. If the workers want the filling process to work so that almost all cans have volumes between12.04 oz and12.56 oz, the range rule of thumb can be used to estimate that the standard deviation should be less than0.13oz. Use the sample data to test the claim that the population of volumes has a standard deviation less than0.13 oz. Use a0.05 significance level. Complete parts(a) through(d) below.

Calculate the value of the test statistic,

i) 2= -------

ii) P=--------

d). A simple random sample of30 filtered100-mm cigarettes is obtained from a normally distributedpopulation, and the tar content of each cigarette is measured. The sample has a standard deviation of0.20 mg. Use a0.05 significance level to test the claim that the tar content of filtered100-mm cigarettes has a standard deviation different from0.30 mg, which is the standard deviation for unfilteredking-size cigarettes. Complete parts(a) through(d) below.

Calculate the value of the test statistic.

2=

P- value=

e). Test the given claim. Assume that a simple random sample is selected from a normally distributed population. Use either theP-value method or the traditional method of testing hypotheses.

Company A uses a new production method to manufacture aircraft altimeters. A simple random sample of new altimeters resulted in errors listed below. Use a 0.05 level of significance to test the claim that the new production method has errors with a standard deviation greater than 32.2ft, which was the standard deviation for the old production method. If it appears that the standard deviation isgreater, does the new production method appear to be better or worse than the oldmethod? Should the company take anyaction?

40, 75, 24, 73, 41, 15, 16, 52, 7,54, 109, 109

Calculate the value of the test statistic,

i) 2= -------

ii) Determine the criticalvalue(s).

The criticalvalue(s) is/are

enter your response here.

Round to two decimal places asneeded

f).The data table contains waiting times of customers at abank, where customers enter a single waiting line that feeds three teller windows. Test the claim that the standard deviation of waiting times is less than1.8 minutes, which is the standard deviation of waiting times at the same bank when separate waiting lines are used at each teller window. Use a significance level of0.05.

Assume that the sample is a simple random sample selected from a normally distributed population. Complete parts(a) through(d) below.

Customer Waiting Times (in minutes)
6.8	7.5	8.9	7.6
6.2	7.3	7.9	6.7
7.5	7.2	6.5	6.8
7.2	7.6	5.1	6.5
6.3	6.5	8.4	7.9
7.9	7.9	7.1	5.9
7.6	8.6	6.8	6.5
6.2	7.8	7.8	6.4
7.9	7.2	6.1	8.8
7.6	7.2	6.1	6.4
6.2	6.2	6.2	8.9
7.7	6.7	7.8	6.9
8.4	6.9	6.3	7.9
7.9	6.7	7.5	7.3
6.5	7.7	7.4	6.6

Calculate the value of the test statistic,

i) 2= -------

ii) P=--------

g)Data show that men between the ages of 20 and 29 in a general population have a mean height of 69.3inches, with a standard deviation of 3.1 inches. A baseball analyst wonders whether the standard deviation of heights ofmajor-league baseball players is less than 3.1 inches. The heights(in inches) of 20 randomly selected players are shown in the table.

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view the data table.

72	74	71	71	76
70	77	75	72	72
77	72	75	70	73
74	75	73	74	74

Calculate the value of the test statistic,

i) 2= -------

ii) P=--------