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Testing of Hypothesis Problems: T test and Z test

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1. Find the critical values for the alternative hypothesis:
H1: p not equal to 0.18 ,alpha =0.09. Assume that the normal distribution applies.
What are the critical values?

2. A student claimed that the proportion of students using the current recreation centre is less than 0.4. A survey of 900 students resulted in 47% saying that they did use the recreation center. Find the test statistic.

3. Suppose a study is conducted to test the claim, at a 0.05 significance level, that a population proportion is 40%. A simple random sample of 750 subjects has a proportion of 42%. Find the test statistic, critical values and p-value.

4. In a study of checkout-scanners, 8 of 650 items were found to be overcharges. Test at the 0.01 significance level, the claim that with scanners, 1% of sales are overcharges. Find the test statistic, critical values.

5. Determine whether the given conditions justify using the methods of this section when testing a claim about the population mean . The simple random sample size is n =15, is not known, and the original population is normally distributed.
Can these methods be used or not?

6. In order to monitor the ecological health of the florida everglades, various measurements are recorded at different times. The bottom temperatures are recorded at the Garfield Bight Station, and the mean of 20.8 degree celcius is obtained for 46 temperatures on 46 different days. Assuming that , test the claim that the population mean is greater than 20.0 degree celcius. Use a 0.05 significance level.
Calculate the test statistic(round to the nearest hundredth) and the p-value. (Round to four decimal places) and conclusion.

7. Determine whether the hypothesis test involves a sampling distribution of means that is a normal distribution, student t distribution or neither
Claim: mean = 50. Sample data: n=35, x-bar =53, and s =5.
The sample data appear to come from a population with a distribution that is not normal with unknown. State only type of distribution.

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Solution Summary

The solution gives the details of students t test and Z test. Null hypothesis, alternative hypothesis, critical value, p value and test statistic is given with interpretations.

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Hypothesis testing problems using Z and t test

The Board of Surgeons recommends a postoperative examination six months after a prostatectomy. In a sample from the records of Carver Memorial Hospital, follow-up exams were given in 80 out of 200 cases. In a sample of records from HiRent Hospital, follow-up exams were given in 120 out of 200 cases.
Normality may be assumed because
the population may be assumed normal.
the population may be assumed large.
the samples may be assumed random.
nπ ≥ 10, n(1-π) ≥ 10 for both samples.

The test statistic is:
-1.96
-2.58
-4.00
-3.477

If we are using α = .01 and a left-tailed test the decision is
clearly reject the hypothesis of equal proportions.
barely reject the hypothesis of equal proportions.
barely accept the hypothesis of equal proportions.
clearly accept the hypothesis of equal proportions.

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