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tennispro154
17.12.2019 •
Mathematics
Consider the following hypothesis test: h 0: = 17h a: 17a sample of 40 provided a sample mean of 14.12. the population standard deviation is 4.a. compute the value of the test statistic (to 2 decimals). (if answer is negative, use minus "-" sign.)b. what is the p-value (to 4 decimals)? c. using = .05, can it be concluded that the population mean is not equal to 17? selectyesnoitem 3answer the next three questions using the critical value approach.d. using = .05, what are the critical values for the test statistic (to 2 decimals)? ±e. state the rejection rule: reject h 0 if z is selectgreater than or equal togreater thanless than or equal toless thanequal tonot equal toitem 5 the lower critical value and is selectgreater than or equal togreater thanless than or equal toless thanequal tonot equal toitem 6 the upper critical value.f. can it be concluded that the population mean is not equal to 17?
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Ответ:
We conclude that the population mean is not equal to 17.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 17
Sample mean,
= 14.12
Sample size, n = 40
Alpha, α = 0.05
Population standard deviation, σ = 4
First, we design the null and the alternate hypothesis
We use Two-tailed z test to perform this hypothesis.
a) Formula:
Putting all the values, we have
b) P-value can be calculated from the standard z-table.
P-value = 0.0000
c) Since the p-value is less than the significance level, we reject the null hypothesis and accept the alternate hypothesis. Thus, the population mean is not equal to 17
d) Now,![z_{critical} \text{ at 0.05 level of significance } = \pm 1.96](/tpl/images/0421/9510/83863.png)
e) Rejection Rule:
We reject the null hypothesis if it is less than lower critical value and greater than the upper critical value
If the z-statistic lies outside the acceptance region which is from -1.96 to +1.96, we reject the null hypothesis.
f) Since the calculated z-stat lies outside the acceptance region, we reject the null hypothesis and accept the alternate hypothesis. Thus, the population mean is not equal to 17.
Ответ:
Step-by-step explanation:
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