For each of the following situations determine which hypothesis test procedure i
ID: 3276110 • Letter: F
Question
For each of the following situations determine which hypothesis test procedure is the most appropriate. The significant level is 0.05 You DO have to perform the test, following 5 steps procedure. The hypothesis test procedures you have a choose from are One sample Z-test for proportions wo sample Z-test for proportions One sample t-test for means Two sample t-test for means Paired t-test a. A committee at the College Board has been asked to study the SAT math scores for students in Pennsylvania and Ohio. A sample of 45 students from Pennsylvania had an average score of 580, whereas a sample of 38 students had an average score of 530. The sample standard deviations for Pennsylvania and Ohio are 105 and 114 respectively. Does the study suggest that the SAT math score for students in Pennsylvania and Ohio differ? b. A field biologist examined the sex ratio at birth of the lesser snow geese. A random sample of nests containing four eggs was taken. For each egg resulting in a live gosling, the laying order and the gender of the gosling were recorded Of the 27 successfully hatched first eggs, 17 were male. Is there significant evidence that the proportion of male goslings is not 50% c. A manufacturer claims that a new design for a portable phone has increased the phone's range to 150 feet, allowing many customers to use the phone throughout their homes and yards. An independent testing laboratory found that a random sample of 44 of these phones worked over an average distance of 142 feet, with a standard deviation of 12 feet. Is there evidence that the manufacturer's claim is false d. In 2001, one county reported that, among 3132 white women who had babies, 94 were multiple births. There were also 20 multiple births to 606 black women Does this indicate any racial difference in the likelihood of multiple births?Explanation / Answer
a). The appropriate test procedure for this problem is two sample t-test for means (two tailed).
Hypothesis H0: The SAT math scores for students in Pensylvania and Ohio do not differ.
We will assume that the standard deviations for the 2 populations from Pensylvania and Ohio are equal. This is a standard assumption in two sample t-test.
Suppose n1 and n2 are the sample sizes, m1 and m2 are the sample means, and s1 and are the sample standard deviations.
The pooled standard deviatiion is given by the formula: sp = sqrt(((n1-1)s12 + (n2-1)s22)/(n1+n2-2))
Here n1 = 45, n2 = 38, m1 = 580, m2 = 530, s1 = 105, s2 = 114
Hence pooled standard deviation, sp = sqrt((44 x 105 x 105 + 37 x 114 x 114)/81)
= sqrt (( 485100+480852)/81) = 109.20
t-statistic is given by the formula t = (m1-m2)/sp.sqrt(1/n1+1/n2) and degrees of freedom = (n1+n2-2).
Hence t-statistic value = (580-530)/(109.20 x sqrt(1/45 + 1/38)) = 50/(109.2 x 0.22) = 2.08
degrees of freedom = 45 + 38 - 2 = 81.
Probability value corresponding to this t value, using the TDIST function in Excel for 81 df and 2 tails = 0.040687, which is less than the given significance level 0.05.
Hence we reject the hypothesis and conclude that the SAT math scores of pensylvania and ohio are different.
b) The appropriate test in this case is one sample Z-test for proportions (one tailed test).
Hypothesis H0: proportion of male goslings in eggs hatched, P = 0.5 (50%)
sample size n = 27 and sample proportion p = 17/27 = 0.6296
test statistic is calculated by the formula z = (p - P) / sqrt(P(1-P)/n)
hence in this case z value = (0.6296-0.5)/sqrt(0.5 x 0.5 /27) = 0.1296 / 0.0962 = 1.3472
Probability of getting or exceeding this value is 0.0890 using NORMDIST function in Excel, which is > 0.05.
Hence we accept the hypothesis that the male proportion is 0.5 or 50%.
c) Appropriate test in this case is one sample t-test for means (one tailed).
Formula for t-statistic = (m - M)/sqrt(s2/(n-1))
Here M= 150, n = 44, m = 142, s = 12.
Hence calculated value of t = 150 / sqrt (144/43) = 150/1.83 = 81.97 with 43 degrees of freedom.= 3.59E-49 from Excel formula. Hence we reject the hypothesis
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