Find the rejection region for the standardized test statisti

Find the rejection region (for the standardized test statistic) for each hypothesis test.

H0:=17 vs. Ha:<17 @ =0.01.

H0:=880 vs. Ha:880 @ =0.01.

H0:=12 vs. Ha:>12 @ =0.05.

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The recommended daily calorie intake for teenage girls is 2,200 calories/day. A nutritionist at a state university believes the average daily caloric intake of girls in that state to be lower. Test that hypothesis, at the 5% level of significance, against the null hypothesis that the population average is 2,200 calories/day using the following sample data: n = 36, x=2,150, s = 203.

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The labor charge for repairs at an automobile service center are based on a standard time specified for each type of repair. The time specified for replacement of universal joint in a drive shaft is one hour. The manager reviews a sample of 30 such repairs. The average of the actual repair times is 0.86 hour with standard deviation 0.32 hour. Test at the 1% level of significance the null hypothesis that the actual mean time for this repair differs from one hour.

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The mean increase in word family vocabulary among students in a one-year foreign language course is 576 word families. In order to estimate the effect of a new type of class scheduling, an instructor monitors the progress of 60 students; the sample mean increase in word family vocabulary of these students is 542 word families with sample standard deviation 18 word families.

Test at the 5% level of significance whether the mean increase with the new class scheduling is different from 576 word families, using the critical value approach.Compute the observed significance of the test.

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Find the rejection region (for the standardized test statistic) for each hypothesis test based on the information given. The population is normally distributed.

H0:=880 vs. Ha:880 @ =0.01, n = 4, unknown

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A dairy farm uses the somatic cell count (SCC) report on the milk it provides to a processor as one way to monitor the health of its herd. The mean SCC from five samples of raw milk was 250,000 cells per milliliter with standard deviation 37,500 cell/ml. Test whether these data provide sufficient evidence, at the 10% level of significance, to conclude that the mean SCC of all milk produced at the dairy exceeds that in the previous report, 210,250 cell/ml. Assume a normal distribution of SCC.

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In the past, 68% of a garage’s business was with former patrons. The owner of the garage samples 200 repair invoices and finds that for only 114 of them the patron was a repeat customer. Test whether the true proportion of all current business that is with repeat customers is less than 68%, at the 1% level of significance. Compute the observed significance of the test

Solution

H0: =17 vs. Ha:<17 @ =0.01...

Reject H0 if x-bar < 17 + ( -2.326348 * population s.d)

H0:=880 vs. Ha:880 @ =0.01.....

reject H0 if x-bar > 880 + ( 2.575829*population s.d) or, x-bar is < + ( -2.575829*population s.d)

H0:=12 vs. Ha:>12 @ =0.05.

reject H0 if x-bar> -12 + ( 1.644854* population s.d)

2) H0: mean=2200 ag H1: mean < 2200...
n = 36, x-bar=2,150, s = 203.

test statistics = (2150-2200) / (203/ sqrt(36) ) = -1.477833.......

p-value = 0.1483957......which is less than <0.05..

so, null hypothesis is true...population average is 2,200 calories/day....