Question

Use the t-distribution table to find the critical value(s) for the indicated alternative hypotheses, level of significance a, and sample sizes n1 and n2. Assume that the samples are independent, normal, and random Answer parts (a) and (b) Ha H1H2, 0.005, n1 12, n2 10 (a) Find the critical value(s) assuming that the population variances are equal. Construct a 90% confidence interval for -H2 with the Bakery A Bakery B sample statistics for mean calorie content of two bakeries specialty pies and confidence interval construction formula below. Assume the populations with equal variances 1659 cal 1891 cal x1 x2 S1 = 159 cal S2 206 cal approximately normal are 12 n1 = 6 n2 1 1 1 + Confidence n2 n1 n2 nt interval when (n-1) (n2-1) variances are and d.f. n +n2-2 where a equal = n1+n2-2 Enter the endpoints of the interval (Round to the nearest integer as needed.) A marine biologist claims that the mean length of mature female pink seaperch is different in fall and winter. A sample of 10 mature female pink seaperch collected in fall has a mean deviation of 15 millimeters. A sample of 2 mature female pink seaperch collected in winter has a 100 millimeters and a standard deviation of 11 millimeteers. At o 0.20, claim? Assume the population variances populations are normally distributed. Complete parts (a) through (e) below length of 118 millimeters and a standard mean length of can you support the marine biologist's random and independent, and the are equal. Assume the samples are Which hypothesis is the claim? The alternative hypothesis, Ha The null hypothesis, Ho (b) Find the critical value(s) and identify the rejection region(s) Enter the critical value(s) below. (Type an integer needed.) or decimal rounded to three decimal places as needed. Use a comma to separate answers as

Answer 1

1)

given hypothesis test is one tailed test hence for a given level of significance 0.005, and degrees of freedom 10+12-2= 20

critical value t_0.005,20 = 2.845

2) Bakery problem

Two-Sample T-Test and CI

Method

μ₁: mean of Sample 1

µ₂: mean of Sample 2

Difference: μ₁ - µ₂

Equal variances are assumed for this analysis.

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
Sample 1	6	1891	159	65
Sample 2	12	1659	206	59

Estimation for Difference

Difference	Pooled StDev	90% CI for Difference
232.0	192.5	(63.9, 400.1)

Test

Null hypothesis	H₀: μ₁ - µ₂ = 0
Alternative hypothesis	H₁: μ₁ - µ₂ ≠ 0

T-Value	DF	P-Value
2.41	16	0.028

90% CI for Difference = (64, 400)

3) given n1 = 10, n2 = 2 given population variances are equal

degrees of freedom = n₁+n₂-2 = 10

level of significance = 0.20

two tailed test

critical value = t_0.1,10 = 1.372